{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classification (2) – implementation and application of Nearest Neighbour classification, and Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we continue on with some of methods of \n",
    "classification, starting with an implementation of Naive Bayes, then an application of Naive Bayes on a benchmark dataset. The notebook also looks into the related method of Logistic Regression for comparison."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification\n",
    "Classification models learn a mapping $h(\\boldsymbol{X})$ from a feature space $\\boldsymbol{X}$ to a finite set of labels $\\boldsymbol{Y}$\n",
    "\n",
    "\n",
    "In this lab we will focus for simplicity on binary classification, where the labels are assumed to be in $\\{-1,1\\}$ or alternatively $\\{0,1\\}$. \n",
    "\n",
    "\n",
    "We will use simple generated datasets and a real data set on the sinking of the Titanic to explore some different classification algorithms. For a description of the variables and more information on the data see: https://www.kaggle.com/c/titanic-gettingStarted/data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "version 1\n",
      "SKLEARN 0.20.1\n",
      "SCIPY 1.1.0\n",
      "NUMPY 1.15.4\n",
      "MATPLOTLIB 3.0.2\n",
      "579\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "%load_ext autoreload\n",
    "%autoreload\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as pl\n",
    "import util\n",
    "\n",
    "from scipy.stats import itemfreq\n",
    "from scipy.stats import bernoulli\n",
    "from scipy.stats import multivariate_normal as mvnorm\n",
    "\n",
    "import sklearn\n",
    "import scipy\n",
    "import matplotlib\n",
    "print(\"SKLEARN\",sklearn.__version__)\n",
    "print (\"SCIPY\",scipy.version.full_version)\n",
    "print(\"NUMPY\",np.__version__)\n",
    "print(\"MATPLOTLIB\",matplotlib.__version__)\n",
    "\n",
    "X, Y = util.load_data() # passenger_class, is_female, sibsp, parch, fare, embarked (categorical 0-3)\n",
    "X_demean = X - np.mean(X, axis=0)\n",
    "X_unitsd = X_demean/(np.std(X_demean,axis=0))\n",
    "X_whiten = np.dot(X_demean, util.whitening_matrix(X_demean))\n",
    "print(len(X[:,:2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One approach to learning a classification function $h(\\boldsymbol{X})$ is to model $P(y|\\boldsymbol{x})$ and convert that to a classification by setting:\n",
    "\\begin{equation}h(\\boldsymbol{X}) = \\begin{cases} 1 & \\text{if }P(y|\\boldsymbol{x}) > \\frac{1}{2}\\\\ 0 & \\text{otherwise}\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "Example: Suppose we want to build a model to predict the probability of survival on the Titanic based on just two categorical features, a persons class (1,2 or 3) and their sex (1=female,0=male). An obvious approach would be to create a category for each combination of our features (female 1st, female 2nd ... male 3rd) and calculate the proportion who survived in each as an estimate for the survival probability $P(y|\\boldsymbol{x})$. For each observation in our test data - we simply look up the survival rate in the corresponding category.\n",
    "\n",
    "This corresponds to maximum likelihood estimation: $\\hat{\\theta} = argmax_{\\theta'}P(data|\\theta')$, where the parameters, $\\theta$, we want to estimate are the true probabilities $P(y|\\boldsymbol{x})$ for each combination of $\\boldsymbol{x}$ and $data$ is the set features and labels we have observed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "combin is  [(1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1)]\n",
      "(1, 0) 0.38961038961038963\n",
      "(1, 1) 0.9846153846153847\n",
      "(2, 0) 0.1780821917808219\n",
      "(2, 1) 0.9122807017543859\n",
      "(3, 0) 0.14218009478672985\n",
      "(3, 1) 0.4583333333333333\n"
     ]
    }
   ],
   "source": [
    "combinations = [(i,j) for i in [1,2,3] for j in [0,1]]\n",
    "print(\"combin is \",combinations)\n",
    "for c in combinations:\n",
    "    match = np.where((X[:,0] == c[0]) * (X[:,1] == c[1]))[0]\n",
    "    print(c,sum(Y[match])/float(len(match)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question:** *Why will this approach not work in general? What happens as we increase the number of features or the number of values each feature can take? What about if features are continuous?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.it has very low efficiency, it loops through the whole dataset for every iteration.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naive Bayes\n",
    "\n",
    "\n",
    "Following Bayes Rule, we can write:\n",
    "\n",
    "$P(y|\\boldsymbol{x}) \\propto P(y)P(\\boldsymbol{x}|y) = P(y)P(x_1,x_2...x_D|y) $\n",
    "\n",
    "It easy to estimate $P(y)$ as just the proportions of each class in the training data. We could also directly estimate $P(x_1,x_2...x_D|y)$ for each $y$ (for example with kernel density estimation) but as the number of features $D$ gets large this estimation suffers the curse of dimensionality.\n",
    "\n",
    "Naive Bayes assumes that the data was generated by a model where all the features are independent of one-another given the class label so that we can estimate $P(x_j|y)$ separately for each feature.\n",
    "\n",
    "\\begin{equation}\n",
    "P(y|\\boldsymbol{x}) \\propto P(y)\\prod_{j=1}^D P(x_j|y)\n",
    "\\end{equation}\n",
    "\n",
    "The normalisation constant can be obtained;\n",
    "\n",
    "\\begin{equation}\n",
    "P(y|\\boldsymbol{x}) = \\frac{P(y)\\prod_{j=1}^D P(x_j|y)}{P(\\boldsymbol{x})},\n",
    "\\end{equation}\n",
    "where,\n",
    "\\begin{equation}\n",
    "P(\\boldsymbol{x}) = P(y=0)\\prod_{j=1}^D P(x_j|y=0) + P(y=1)\\prod_{j=1}^D P(x_j|y=1),\n",
    "\\end{equation}\n",
    "this operation is called [marginalisation](http://en.wikipedia.org/wiki/Marginal_distribution), since we marginalise (or sum/integrate out) $y$ from the joint distribution (top line) $P(y, \\mathbf{x}) = P(y)P(\\mathbf{x}|y)$ to obtain a distribution over $\\mathbf{x}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** *Implement a Naive Bayes model for the Titanic data set using passenger_class and is_female as features*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(579, 6)\n",
      "(579,)\n",
      "(1, 0) 0.4243339521922548\n",
      "(1, 1) 0.8891634908224024\n",
      "(2, 0) 0.2734674433208462\n",
      "(2, 1) 0.8037866248511775\n",
      "(3, 0) 0.10677887360860094\n",
      "(3, 1) 0.5654123815352137\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Applications/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:4: DeprecationWarning: `itemfreq` is deprecated!\n",
      "`itemfreq` is deprecated and will be removed in a future version. Use instead `np.unique(..., return_counts=True)`\n",
      "  after removing the cwd from sys.path.\n"
     ]
    }
   ],
   "source": [
    "# a function that may be useful\n",
    "def proportions(array):\n",
    "    \"\"\" returns a map from each unique value in the input array to the proportion of times that value occures \"\"\"\n",
    "    prop = itemfreq(array)\n",
    "    prop[:,1] = prop[:,1]/sum(prop,axis=0)[1]\n",
    "    return dict(prop)\n",
    "\n",
    "class Naive_Bayes:\n",
    "    def train(self,X,Y):\n",
    "        \"\"\" trains the model with features X and labels Y \"\"\"\n",
    "        # 1) Estimate P(Y=1)\n",
    "        self.py = sum(Y)/float(len(Y))\n",
    "\n",
    "        # 2) For each feature, x, estimate P(x|y=1) and P(x|y=0)\n",
    "        survived = X[np.where(Y==1)[0],:] # the features of those who survived\n",
    "        died  = X[np.where(Y==0)[0],:] # the features for those who died\n",
    "\n",
    "        # estimate P(gender|survived)\n",
    "        self.gs = proportions(survived[:,1]) # return a map from gender value to probability: Hint the proportions function above may help\n",
    "\n",
    "        # estimate P(class|survived)\n",
    "        self.cs = proportions(survived[:,0]) # return a map from class to probability for those who survived\n",
    "\n",
    "        # estimate P(gender|died)\n",
    "        self.gd = proportions(died[:,1]) # return a map from gender value to probability for those who died\n",
    "\n",
    "        # estimate P(class|died)  \n",
    "        self.cd = proportions(died[:,0]) # return a map from class to probability for those who died\n",
    "    \n",
    "    def predict(self,sex,p_class):\n",
    "        \"\"\" outputs the probability of survival for a given class and gender \"\"\"\n",
    "        # caclulate unormalized P(y = 1|sex,p_class) as P(y=1)P(sex|y=1)P(p_class|y=1) \n",
    "        ps = self.py * self.gs[sex] * self.cs[p_class]\n",
    "\n",
    "        # calculate unormalized P(y = 0|sex,p_class) as P(y=0)P(sex|y=0)P(p_class|y=0)\n",
    "        pd = (1 - self.py) * self.gd[sex] * self.cd[p_class]\n",
    "\n",
    "        # calculates the survival ratio as ps/pd and the normalized probability  from the ratio\n",
    "        r = ps/pd\n",
    "        psn = r/(1+r)\n",
    "        return psn\n",
    "\n",
    "# run the model\n",
    "model = Naive_Bayes()\n",
    "print(X.shape)\n",
    "print(Y.shape)\n",
    "model.train(X,Y)\n",
    "for p_class,sex in combinations:\n",
    "    print((p_class,sex),model.predict(sex,p_class))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** *Compare these predictions with those just based on the proportion of survivals. How true is the Naive Bayes assumption for this case?*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "combin is  [(1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1)]\n",
      "(1, 0) 0.38961038961038963\n",
      "(1, 1) 0.9846153846153847\n",
      "(2, 0) 0.1780821917808219\n",
      "(2, 1) 0.9122807017543859\n",
      "(3, 0) 0.14218009478672985\n",
      "(3, 1) 0.4583333333333333\n"
     ]
    }
   ],
   "source": [
    "combinations = [(i,j) for i in [1,2,3] for j in [0,1]]\n",
    "print(\"combin is \",combinations)\n",
    "for c in combinations:\n",
    "    match = np.where((X[:,0] == c[0]) * (X[:,1] == c[1]))[0]\n",
    "    print(c,sum(Y[match])/float(len(match)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#How to judge \"how true the NB assumption is\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question:** *How does the number of parameters to be learnt scale with the number of features for Naive Bayes?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the number of features increases, the number of parameters to be learnt will be increased as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** *Run Naive Bayes from Sci-Kit Learn using the same features.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Applications/anaconda3/lib/python3.7/site-packages/sklearn/preprocessing/_encoders.py:368: FutureWarning: The handling of integer data will change in version 0.22. Currently, the categories are determined based on the range [0, max(values)], while in the future they will be determined based on the unique values.\n",
      "If you want the future behaviour and silence this warning, you can specify \"categories='auto'\".\n",
      "In case you used a LabelEncoder before this OneHotEncoder to convert the categories to integers, then you can now use the OneHotEncoder directly.\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "OneHotEncoder(categorical_features=None, categories=None,\n",
       "       dtype=<class 'numpy.float64'>, handle_unknown='error',\n",
       "       n_values=None, sparse=True)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import OneHotEncoder\n",
    "nb_enc = OneHotEncoder()\n",
    "X_train_ohe = nb_enc.fit(X[:,:2])\n",
    "X_train_ohe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 0) 0.4226630709701513\n",
      "(1, 1) 0.8863892268829936\n",
      "(2, 0) 0.27410238327333064\n",
      "(2, 1) 0.8009625562382566\n",
      "(3, 0) 0.10796095358725434\n",
      "(3, 1) 0.5632808975188677\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import OneHotEncoder\n",
    "from sklearn.naive_bayes import MultinomialNB\n",
    "\n",
    "# Sklearn doesn't have a model that expects categorical data. \n",
    "# We need to first encode our (p_class, sex) to (is_first,is_second,is_third,is_female,is_male)\n",
    "\n",
    "# use preprocessing.OneHotEncoder to create a new dataset X2 that is the transformation of the first 2 columns of X\n",
    "\n",
    "nb_enc = OneHotEncoder(categories='auto')\n",
    "X2 = nb_enc.fit_transform(X[:,:2]).toarray()# use the encoder to transform the first two columns of X \n",
    "\n",
    "# fit a Multinommial Naive Bayes Model\n",
    "nb = MultinomialNB()\n",
    "nb.fit(X2, Y)\n",
    "\n",
    "\n",
    "# transforms our combinations to the one-hot encoding\n",
    "c = nb_enc.transform(np.asarray(combinations)).toarray()\n",
    "\n",
    "# gets predictions for each combination\n",
    "predictions = nb.predict_proba(c)\n",
    "\n",
    "# prints your predictions in the same format as previous models\n",
    "for i in range(len(c)):\n",
    "    print(combinations[i],predictions[i][1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Naive Bayes can also handle continuous features. The data below is generated by a ```Gaussian mixture model```. For each class there is a separate 2-dimensional Gaussian distribution over the features x1, x2. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generates some data from a Gaussian Mixture Model. \n",
    "mean0 = [-1,-1]  # the mean of the gaussian for class 0      \n",
    "mean1 = [1,1] # the mean of the gaussian for class 1\n",
    "cov0 = [[.5, .28], [.28, .5]]#[[.5, .28], [.28, .5]] # the covariance matrix for class 0\n",
    "cov1 = [[1, -.8], [-.8, 1]]#[[1, -.8], [-.8, 1]] # the covariance matrix for class 1\n",
    "mixture = util.GaussianMixture(mean0,cov0,mean1,cov1)\n",
    "mX,mY = mixture.sample(500,0.5,plot=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** *Fit a Gaussian Naive Bayes model using Sklearn*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "\n",
    "# fit a GaussianNB model\n",
    "\n",
    "gnb = GaussianNB() # create and fit a Gaussian Naive Bayes model to the Gaussian mixture data mX,mY\n",
    "gnb.fit(mX, mY)\n",
    "\n",
    "# plots the probability that a point in x,y belogs to the class Y=1 according to your model and the decision boundary p=.5\n",
    "x = np.linspace(-4,4,100)\n",
    "y = np.linspace(-4,4,100)\n",
    "test_points = np.dstack(np.meshgrid(x, y)).reshape(-1,2)\n",
    "z = gnb.predict_proba(test_points)[:,1].reshape(len(x),len(y)) # probability Y = 1\n",
    "f,ax = subplots(1,1,figsize=(5,5))\n",
    "cn = ax.contourf(x,y,z)\n",
    "ct = ax.contour(cn,levels=[0.5])\n",
    "ax.scatter(mX[:,0],mX[:,1],s=5, c = [\"black\" if t < 1 else \"white\" for t in mY],alpha=1)\n",
    "ax.clabel(ct)\n",
    "show()\n",
    "\n",
    "# Try changing the covariance matrices and refitting your model. \n",
    "# When does the probability distribution returned by Naive Bayes resemble the true one???????\n",
    "# change the covariance larger "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression\n",
    "\n",
    "Logistic regression models $P(y|\\boldsymbol{x})$ directly by assuming it is a (logistic) function of a linear combination of the features. The logistic function $\\theta(s) = \\frac{e^s}{e^s+1}$ maps the weighted features to $[0,1]$ to allow it to model a probability. Training logistic regression corresponds to learning the weights $\\boldsymbol{w}$ to maximise the likelihood function:\n",
    "\n",
    "\\begin{equation}\n",
    "P(y_1...y_n|\\boldsymbol{x}_1...\\boldsymbol{x}_n,\\boldsymbol{w}) = \\prod_{i=1}^n \\theta(y_i\\boldsymbol{w}^T\\boldsymbol{x}_i)\n",
    "\\end{equation}\n",
    "\n",
    "Maximising the likelihood $P(y_1...y_n|\\boldsymbol{x}_1...\\boldsymbol{x}_n,\\boldsymbol{w})$ is equivalent to minimising the negative log-likelihood: \n",
    "\\begin{equation}\n",
    "\\boldsymbol{w}^* = argmin_{\\boldsymbol{w}}\\left( -\\log\\left(\\prod_{i=1}^n \\theta(y_i\\boldsymbol{w}^T\\boldsymbol{x}_i)\\right)\\right)\n",
    "= argmin_{\\boldsymbol{w}}\\left( \\sum_{i=1}^n \\ln(1+e^{-y_i\\boldsymbol{w}^T\\boldsymbol{x}_i})\\right)\n",
    "\\end{equation}\n",
    "\n",
    "Once we have the weights $\\boldsymbol{w}^*$, we can predict the probability that a new observation belongs to each class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question:** *Suppose that we have a data set that is linearly separable. What happens to the weights $w$ when we run linear regression?*\n",
    "**Ans:** *Overfitting*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** *Use Sklearn to fit a logistic regression model on the Gaussian mixture data.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Run Logistic regression on the gaussian mixture data\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "logistic = LogisticRegression(random_state=0, solver='lbfgs',multi_class=\"ovr\").fit(mX, mY) # create and fit a logistic regression model on mX,mY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the probability y = 1 as over the feature space as for Naive Bayes\n",
    "logistz = logistic.predict_proba(test_points)[:,1].reshape(len(x),len(y)) # probability Y = 1\n",
    "f,ax = subplots(1,1,figsize=(5,5))\n",
    "cn = ax.contourf(x,y,logistz)\n",
    "ct = ax.contour(cn,levels=[0.5])\n",
    "ax.scatter(mX[:,0],mX[:,1],s=5, c = [\"black\" if t < 1 else \"white\" for t in mY],alpha=1)\n",
    "ax.clabel(ct)\n",
    "show()# implement the jacobian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2.98483946e-06  2.67555220e+00  2.42601277e+00  6.67001158e-01\n",
      "  -7.32264129e-01  8.65517206e-01]]\n"
     ]
    }
   ],
   "source": [
    "# we can model more complex decision boundaries by expanding the feature space to include combinations of features\n",
    "\n",
    "# re-fit logistic regression adding in all quadratic combinations of features ie x1,x2,x1x2,x1^2,x2^2\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_expand = PolynomialFeatures(2) # create a polynomial feature transformer that produces quadratic combinations\n",
    "m2X = poly_expand.fit_transform(mX) # use poly_expand to transform the original features (mX)\n",
    "logistic.fit(m2X, mY) # fit the logistic model with the new features\n",
    "\n",
    "# transform the test plots and predict and plot\n",
    "testpoints2 = poly_expand.transform(test_points)\n",
    "logistic2z = logistic.predict_proba(testpoints2)[:,1].reshape(len(x),len(y)) # probability Y = 1\n",
    "f,ax = subplots(1,1,figsize=(5,5))\n",
    "cn = ax.contourf(x,y,logistic2z)\n",
    "ct = ax.contour(cn,levels=[0.5])\n",
    "ax.scatter(mX[:,0],mX[:,1],s=5, c = [\"black\" if t < 1 else \"white\" for t in mY],alpha=1)\n",
    "ax.clabel(ct)\n",
    "show()\n",
    "print(logistic.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With large numbers of features there is a risk of overfitting to the training data. We can tune a logistic regression model to reduce the risk of overfitting by penalising large weights, $\\boldsymbol{w}$ \n",
    "\n",
    "**Exercise:** *Experiment with the regularisation parameters sklearn provides: \n",
    "penalty = \"l1\" or \"l2\" and C = inverse of weight of regularisation term.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v3ONuKPseTttcfM6TCbg/OGw5m1pLVeAqHFoj9aH/HGGKW6Qt8m3yejPp/PtEUjsmPnZtFovr32Vxw0qC7o+Oe7y62YtAwZQ5dKNr3PUtBjNp4ZNS/l1KKaSUS6WUB/e9ni7F4Cz2XhThZn7tX6kP3cz82r8ACtH0k6Tzy8nrbQhh48D6d/A6jitBb5L1HWfSm/wteb2DZO6fOGxzUBU3tcEbRqk7eD05W1iPYaYRCFQlSH3oFlxDCLVhxjBlFsNMo5u9Q7rm7Uw6/w5r2paxqfN8DBnrv+53nY6iuFCEnUrf58d0xwPHu5am7ktoj95CU7d1zrAUWJ4bFhNCVQIowokiHCjSjhB2TJliU9cnKPdeTF3wW8VQ8qFvsKHjQyXoURJwn4amVBBwnwFSYJp5EtlXh61RE7iRKv+/kMm/x8bOC/oztW3ruZqA+0PoZpjZFb9GUZyEPOexsmUxO6/HmTLN+vYz8TqPJpEZvGY5VhLZl6iR12MCvcnfTqiNVO51K59vCbF8dS0mRMFopyt2G7nCVloj/zXAlSydfx/6goqmsqU82VTcYBHbrTghKRgdAARcZ7Gw9iXqgt/uL13pvxwhBA7bXFz2D+zUSo5o+nGy+TX9CdoECkNlaysYrURSf0A3e/qvCRy47EtHnfpuJ1dYz+rWw1nTegzh1APjuWGL3YRl8VlMmM74T+iM/2TQ9Ux+Oes7PoimVpHKlU74mro+TWPZj3DZFyOEisRA68uV0Vj+Y1TFQ5laQyT9GJn8cuKZ5/E7T8I0k2QL64DiFN2uzSBbWI9udrO1518Ius+lN3k/u7rWOW0LqQ/dTE5vojX89b44gYJ5NU9h1xopGB2saz+FsezamjLVF0bfYm/AEj6L3UIxF0dTSdvMFtbitC9CCBVT6iSz/6Aj9n1AkNe34dBmAhK9zwrc2nMlDm0uBaMFU2ZQhIcFtS+iKQGSuX+yufszxDPPDev90Vj2Q1z2D+CyLyGVe51I6g+oSgCnbQ5CaAjRgKZWWHl290Gsqa7FPkUq9waGmcI0o2zt+Rcay37A0sat2LXZZPXNbOw4v3/6C5KcvqH/CElxQ8SPorjwOUffdMkbrUhZXBcs6EVxM8wokdQfkdIgln56wqKnCDdV/qso81zE7k+IbrErlsVnsU/R1HUxbvsHyBWaUBUfPtfJCCFQhROHNgubVktWH9pNPJNfTSb/Ph7HEXTHfzlqX8291xHyfJy8vo1k7u87roevH9VlbTTqQjcR8pwH0gQMwnvYB3q6YwmfRQlR8DlPRje6yBTe30196KTz7wJgGCnyejMObVbfe4KcvmnEupu6PsZY3e9MmaE3ed8kxzs0quJHoCKRKIpnt/RhMTyW8FmUjPrgTYS8H+932dr9xy901refidO2AE2tIaevH1Mi9L0hTFRr+D+QoQK6EaY38eBUD2faYQmfRclwOZYWXbbMLE7bgj1y7kySI1N4Dwrv7Zb2NaWS6sA15Apb6En+ugQtqngdR5PTt7Kt98slaM9iIljCZ1Ey2iL/xYzyn1EwOiYUbn40/K4zqQ99m3R+OVt7rmIikZ3Hy4zyn+BxLkPKPAWjY9wRZQa3dyt+V9HPeH3HB8dooVqUGkv4LEpGOv8ua9uP323tN5T9Nza1ClUJ4HMePyCGnioCKIqHgtFW4l6VHSuCYvK7r17H4aiKB8NM4bIttIRvirCOs1jsM2TyazDMFMVNjB2Z25y2hSyqf4OFdS9T7v3skHXt2ixmlN9Kpe9LQDHv76yKu/G7hg9SALAtfB29yYfpjP0vsXTR2gu6P0q591IEjnHfQ2vk2+hGhEx+BfHsi+OuP1YU4cXnPBm174C3xUAsi89iD7E9WMDEY9Nt6fk8fudJZAsbBlhKPucJCGFDEXbKPBfQm7xnUN2ZFbfjsi3G7zqdnL6ZmRU/RxE2/K7TWNd+Cjl9E41lP8HnOp6O6A8Ipx4GQDc6aY18vb+dkOeCvqRHCk7bggHvjYVY5klirU9O5PbHxbyaJ7Gp1UiZY03bMRMKh7U/YwmfxZDcH1nW//PFodcm1daM8tsIus8BTDZ1fYbUTmfixoOUWWKZvw66Hkv/lSr/VaD46Ir/YpjKBiBQhBu/85Qd/r6A17kMNe8l4P4gquKmPvRtCkY7Ic/HCCcfJpnbEQhBU8oBFSE0bGrNoG6EcCJQp9Q9TWDHoc1GCAXT1NDUamtKvQuW8E0Tdhay3Vl3sEgKgu5ziol+UKkOXE1T1+jCZ1MbKPNeSCr3T5LZV0Ysmze2sar1YARanz/tYMLJR6krW4wibPhcx9GbfJBy70WYMksi80KfRWRgmCly+mZmVf4SRTgJuM5kZesH+oMw9Cbvp9z7OexaLS77UhTh7U885LYfzJyqR0AobO2+inj2b6Pe53DY1RkUjI4JJSmS5OmI/YhK3xeIpZ+yRG8ILOHbD5mMyO2Ovr9dsxKXbQkA4eQjY2pnTtXvsGv1SJlnXceZ5Hda0xsaOazoAcSyf6PGvB4UL73Jh+mK/4yu+K19MffSAKxrPw2X/QOkcss5sO7vfZ5kA8/8mTKDTatCCBWbWsX82mfZ2PERdLOHoPtcFMUFwKzKX5LIvsDm7kvHdL87M7PiTvyuUykYXaxvP3WYaapK0H0Wuhkd8ouheH8/G3ff0wVL+PZxSiVyM9zzUITCltS6krS3M/+55mZmuRcQ1yP05ju5ODR6HVXxFiOwSIkqJu/ZoBsdrG49ElXx9YeYKhjtA8oUjDYKmeKucFP3xX3pNB/rt/YU4UIIJz2Je6j0fQEhBDalgqD7bHqS9xBN/5ly76eL010h8DmPR1MqBoS0GgsB1xkIoaEp5ThsC8jklw8qUxu8kXLvxQhgW++1Qy4BWAyPJXz7IKW26A4NHsfHGq4AAX9uvY9/hIfPVTsRJJLN6R2Juseyfri5+zKqA9eQyLxUstSMkhw+17lU+i6jN/nbITdBagL/RpnnE/Qk76Gg9zKz4i4MI4xuRnA7liKEjZbw1+mK30al73JAkOpzoUvn32FV66HMqf49Tts8svm16GbvsONRhI/60LcRwk5r5JsYZgSgbxp+MTm9iWx+aL9jp20+inAi0bFrsyf9bKYbophrdM+yeKldPvRk9R7vd19ld09dP1r/OZaVn4FA8E7kFR5u/vlu7W84RttEyWYlv74tjqLAZV/y43AWz9WpSlmfaEgEdmZX3oPL8QHawjcRST/aX18RbpY0rEQIG6bMsab1aDS1HMNMUjBa0ZQqFtX/A0XY+3PxCiH68vGaFFNLKqRy77Cx81xc9qXoRpiC0bLLSItJkfJ6M7vuYlf6v0SV7wqi6acwZLIvFL0gnPztgB1iRbhG3Il1aHOZUf5TdLOXbT1XDwh1P505eGbL21LKw0crZ1l8eyl7cp3u5e6nmOddgoLKc12l97gYK6NZgnf+JMYDv04iAN2Aq78WYHblvficJ5DOr2Bj5/l4nctwOw5FVTzUhf6LSPpRPPajqS/7bl+ujVSfpVQg5P4ENcHrAElT92dI597DNBNI4cQ0k2hqVX/fUhZACKQU9CR+A0AmP5ybnDHkhoLATm3g3xBCpczzCboTd/ftNoOUeWZW3ElB76Q9+l0U4cXvOo1k9h9DTpVz+kY2dH54zM/WYiCW8O1lTMXGRDjfxQ/WfXWP9zsS25/DzgJo6IAEKcDQZd8h3RMRQsVlX4JNrSNb2IAiXMW1QcWD13kiB1TehxAKdm0mHdFbAJNE9mUOqHoIRSmW9TiWkcq9ybr20/E4jiSZ+weV3i9Q7ruIVO5t4plniKT+1BcENTmhe5Lkyetb0frO13XFb6NgNAMqftep+JwnIGWBnL6Z6sDVKMKNKdOsaT1qxI0bi/FjCd9ewJ4Qu2e2LdhtbZ8xo/QbItvZWQC/+BU/hlH0HLvyWj+mTJLMvorHeQyZ/Jo+dzUTSQFFODDNPCHXuQhRdFBShI10/h3SfZsFmlrZ14skW9gAFFNZbvfH7Yh/j4749waMZ7IrQ+s7zsbrPJp0bjmmTNCbLObg8NgPRaIjMZGy0JfMyY4i7SiKB8OMTq5jiwFYwjeF7A7Bm4jAldk9XDDzcNbHO3ipc/wiNlSfpRbD7c/qa/85cAq8pecKZlbchU0tx2lbQLawhm0911ITuJ5Y5hnimWcJes5GCI326A/6RQ8gnnkGv/O0YY+E7IpNrcXrPJZE9pUBkZft6gzmVP8eVfGyufuyEfOMmDJBPPPsoOstkRvJFNaimz1EUr/HplZQ5r2I3uQDlujtBqzNjSmglIJXCkvuweOuYFGgloJp8IV/3MN70V0X6ydPqYVw+xS43HspdcFvoihOktl/sqnrgkFlFeFDCHUIARE4tNnkjbYBWeKGQuDgwPo3EcKBKdOsbj2C7dFhqgNfodp/LUKoxDMvsnmI3LcexxGAUtLkSxaDsTY39kJKIXi7Y8rqszlRhEACXtvYUiaOl13HPVkhvD+yjItDr5HXtwImhpkmW1g/ZFlTJgbFHnXaDqQ2eCOZ/Ht0xH44qI4QTvzOk8kW1pHTm1AUT/El7CjShiLcgE5D6Pt4nMcUp6imQSa/dlBbIc8naAh9Bwm0RW4inHpoUvduMXlKInxCiLuBs4EuKeWSUrS5PzFZwdud63MAX3riaW5YdjwrOtt55p/dQGDA+97ZpT8qsf2eJiKAM9xzOb7iLFbGj+Xd9lf5orwUm1pDND3Y+V8IJ7PK78BpX0Bz+AaS2ZcBmFnxC5y2A/A4jiCVe5NsYR26Gem3/GZX/Aa34xBAsL7jDPL6VjpiP6bcexE98XswZZy64LcJes7pO/JSXFus9F1KNP1ofzpLALf9EIRwIBC4HYdYwrcXUCqL7x7gNmD3JCjYR5mM4JVK7JKbA6OWWUs3n3visQm3MRlh3Pk+hxNBVWgcGjyOhB5lbWI5Xzjg67hUD0sCR9Cc3sQdHR1cHHp8yLoB1+l4nEejKh4aQjf3xws0zAimLCD6fImDnnMwzTTrOs5ANzpw2Rf2x81zaLPI61vpjv+c7viOM47bN02Ky0UCRXFgmClsau0A4euO/wKP4wgEgq741JyRtBhISYRPSvmyEGJWKdraH5gqwRskUFKipArYu7Jo4SxaNI8WzaMmC6gpHSWlo+QMRMFE5E2ElMUpoQCpKUibgmlXMN0ahlvD8NnQg/biq9xJvsqJEbAPKYwTEcPhrMDz6y/nkNCxgOSBrT/FkAZSSiQSExMY+vgLQLawAYGCYabIFFb1X9/SfTll3k+RLaylPvTfKMKBFDpexxFE038mmn6WkOccktnXSGRfZSjao/+DwIHDNpNY+hnKvBeSzr9LIvt3FOHpj9CSN7axvuO0cT8Pi92HtcZXQiYqeBMVuwGCY5jY21M4mpM4WtPYW9PYO9Oo6YGeA4ZLxfDZMLw29DIHpl2Q6WjD0HM45sxGcTrAlAhDIgomStZAyeho8TyOlhRqooDYab3MdCjk6jzkG9zkGjxkD/BRqHAOEsPxCOGuAlhur8Im7OiyQMhWyR2bvs0x5aezNv4u4XzXgLrb1/62ky2sI559AY/jcKKpJ/qv62YvXfHbgKIXRG3wBgwzRiL7KuXeSynznI8QKqriZbgQ96ZM0hL5Wv/vPclfoQg/C+texq7W0Rm/lc7Yj8Z836Ph0OZgytROeYMtJsoeEz4hxBXAFQC19eoopfct9pTg7SwmImfg2hLFtTGOc1MCR3MKpVC0fgynSr7OTfLgcgpVLgpVTgrlTvSgHekY+Ozjr71O+L2/IXUdV8VCai68fORBGCZarICtJ4utK4O9I4O9NY3vjW4CrxSPeOg+G9k5PtILg6QXBjGCA63CsYrg9udT5bibTzReSawQ4c3Ii3x6xjUc6D+MgK2MNYl3B9Xb2frzOI7E5zyxONUt+z6x1qcHle9O3EFv8l5MmUNVgtQF/wMh7NufdH85m1qDppQPsBx3xeM4Ak0JIYRKhffSkglfhfcyaoP/DsCmrk+Szr9TknanK3tM+KSUdwF3QfE4y57qd3czEdEbj+D1C4aU2DrTeFZHca+J4mxKIAyJVCDX4CG+rIrcTC/ZGV70cseg/BC+TQoM4XCgh+2EJSAE9ry9WG5EFEAjMd9BZv5OVp0psXWq+21UAAAgAElEQVRmcDUlcDYlcG2M4V0eBiBX7yZ5UDmpg8soVLn672msAvjABi8PbHiQM2asw6cFWOg/GCEEi/yH4NX8JPX4oDqVjjre1L/EMvUpQGCYaXJ607B9bPeLrQl8DSHs/RsW23qvBsBpW8Tc6scRgGEmMWWaLT1XkC2sGdBOOv8OpswgpJ1o+kkctgXMqXwQhEJT12fIFoYOOjAaAfeH+rxMdLzOZZbwTRJrqjtBdqfg7Sx29pYU3hW9eN4LY+8q7jjm6txET6whMy9AdrYP6dxhxfk2KTCO5bXgwkMxClkKyThVh5085npDCWRijptCrZv4sdXFsbdncK+N4n4/TPnTzZQ/3Ux2hofEUVUkDykftxX4zLYFnDljPR2ZZqqc9XRkW0jpiUHlap0zuXred5DS5K22I1nfcTZu+5IhDw7visu+qF/0Iqk/9k8rPY7DESgoihMhXICkJvhvbOn+3ID6hhlhTesxNJT9D+XeTxF0fwRV8QOCuuA3sWsNZPKr2NZ7zbjc0Drjt+K2H4Rhxoim/kTxX1cymVD+05mSHGAWQjwMnARUAJ3Af0oph01Cuq8fYB6v6I1X8LSeLL63evC+04O9K4tUIDM3QGppiNSSEEZwR5Kb0S20qSMxx+z/WY3m8S7vxfdGN472NKZNkDy0gtiJNeTrdsTbG4sAakLhwrlRenNdmEP84x8aPI4LGr6AQ3WyfsN6LvjamTzws7GlovQ4jmZWxS8oGN00dX2qP6yUppQzp/qP2NVGEEW3sq747cMG+/xA40YU4cAws8Xo09LElOm+aDAptvVeRyL7Io1lP8Sm1tISvoGcvnHYce0c0t7rWMbsynuRFNjU+fERp97TjT16gFlK+alStLO3s1sFTzfxrujB/3oXrg1xpIDsHD9dJ9eSWlqG6bEBfUI3fIi3vYqdRTkxx07spFpiJ9Zgb0nhf60L31s9+N/oJjPXT+SMejLz/GOaBuvS5MENfs6Y0T7oPa8WYFX8LZa2H0u5Wsu111zLhldbuT9y3phyh6Ryr7Oq9ZDBfZq9GGYYtHrApD3y38Sz/4ddm9l3iHog0dSfCXrOQcocscyL9CZ+Q7X/ajzOoxEo5PUtlHk+0Rd01ElD2S1s6vr4kGMqTrMfQwgb23q+TNBzPoriREoHIc/HyEQt4Rsv1lR3jIxH9MYieNv/wdVIjrLXtuH/RxdqUqdQ7qD3rEYSR1b0W3Z7s1U3VgaKoJeeC72Ez56B/40uAi91UHf7GjIH+Ih8sIHM/MCYBHDX3d/LZ/87831L6cq28r13r+f+zzxDeEuCZV9cDAze8R0fArvagCLsGGYKVQ2ysPZFAJrDXyWafmJA6ebwV8gVNlIduJag+ywEgi29XyTgOpNsYQPZwlrsWgMgkTJLXt82bM8B15kowo0QCuW+S+lN3I/fdTJISSwz8bwe0xlL+EZhdwmevTlJ8Pl2vCt6QUJ6cYjY8dVk5gVAESWz7ELrxp+sZixEFthHLzQM20UwMUcjekod0RNq8L/eRejZNupuX0N6YYDec2YWd6Y3B0ad/j6zbQFnz9rCAt9BKEKhxtnIuXMvQX1MwSiYaPYda6Bv6l/ikhmXki2sZUvPlaP66G6nJvA1FMWPlAbxzAsE3WcXvTGEIOD68CDhA3YKDloMZCpllmj6T/3vxzPPsaXni9jUGiKp4Q+QxzPPUun/IgKN3uRDxDJPs6b1LSR60Qq1GDeW8I1AKUVvu+A5N8QIPdOKe0Mc06ESO7GW2PE16GWTs+52l8CNp7/xiuGOe1WIH1dD4qgq/H/vJPRMCw0/eI/4MVWEz54xJuvvyS2zuHZeG1WOeoQQLPQdQvXseralN/Fc1x/6y51Xfxl2rRpVCeB3ntofgmpn3PZDAXNAJJdiRjUHEp1sYSV+18n90ZlTudeHHFNv8mFUEUBTy+mM/RS3/WActrlE00/2C24i+8KozylTWMXq1kMRwt4faEE3u0apZTESlvANwe4SvLK/tuDalED32+g9ZwbxY6owXVpRACLjG+OeFrqxsPOYJiaCCrGTa0kcWUnoby0EXunA836EnvNmkurbBR5J/D79ysM8euLn8Gh+3KqHav8hzPEuZltmI+sTKwBozWzGq/kRQhtyM6HM80nqQjchgObwjUTTRUusPXoz9orbMcxoUdCUMip9l5E32ginfj/MiAy6EkUXNZdtCXOqHkEiCbo/MiD7miK8zKy4HZtaS3PvdUNuVpgyDX3Z4CwmjyV8u1Bq0XNsS1L2ZDPu9TH0gI3u82eROLoKaVfGbd3tjWI3HBMVQd8mhcQcjd7zZ5E4opLKR5qouW8jqbd76L7wgBGtv65sghP+VtxlffKUS/BqAYQQZI0dgvHgtp+xwHcwvbkOOnPlgzK+uR1HoAgnIIveHn3Cly2sYV37juM+7dHv0B3/NbrZAZgI7EgMhjteYtcakZioigeHdsCA98o8H8PrOAZFcVIX+vaQobUsSoslfDsxVtEbi+BpvVmqntyA791eDI9Gz0dnEj+2Gmkbn+DtS2I3HOMVwR1rgB5av7KEwMsdlD21jcbvvUfXRXNILw6Nav1d+upj3Lh0Nq2ZLWxLb+i/bkiD1fG3Aah1zuB9uYylym39U8/u+O14HUcgMelO3DVs+zMr7iTgOpNU7k26E79iZsXtmGaGjZ3n7HJQWqPcexFSmsTSz+CyH0hr5BsD2srqTRRDa6UGBDcYD0I4qfJ9sTju+B0TSkQ+nbACkfZRCtFLbg4gsgah51oJvNgOQhA9uZboKbVIpzZmwdsfxG40xmMFJuaY2DoyVN+3AUdbmuiJNQQuOZh/OfpoVuU38ei2t4atO1zElypHPdfNvwUpJVvS68hGzh5lFKLPqsv1ZWtbgxAKpsyRya/G4zgEKXU6Yj+mK35rf63qwFep8l0JQEfsx3Qn7hiydY/jSDS1ilj6L4znULKmVOF2HITXfjTlvksA6Ir/gs74j8fcxv6EFYh0jJTMymvy43m3h4o/bUWLFUgcXkHv2Y0YQYcleEOw/V7HagEm5rhouX4J5X/aRvClDubmNnLCmefxocr5bEh0siLSPGTdZ7YtGFL8yu3VSClxqE6qHQ18d4SjLppaw/yap9GUIM3hG4mkfkcq9wZux6HkCk30Jh/GZT8QKQ0SmRcH1lXKQRS9LDS1bNh7dDsOp8J7CQ7tgGEPRe+KInwsqP0/hNCQMg9CAeROfsYWwzGtha9UVp7Wk6X292txr4uRa/DQ8bn55Gb5xnwkZXcJnmtla8nbzCypL2l7YxXAovhB7wWzyM3yYv/DNq456ka+8di/kmx1k+wcfuo7lPitS6xgdfxtGt1z+GPr3cDw5/z8zlNQhRchbFT5rySS+h2bui7ErjaQN9oAg0T2eaSZxZAx7NosdKMXUyboiP0AVQkCOp2x24Ycn6oEqQ38K0LYqA5cS2/yAaQs4HMeTzq/goIx9N/RptWiCEefD69JT+I+wKAr/tMRn6XFNBa+kojeRj+Bl9oo+0sLKILuC2YV/VS3n8MbhVIK3u4QubH0UyohHIsA9q/9HVZBel41ttvf56snfYuWS+bCouCI6367ip+JwYPbxmZZJXOvIdExZZZwavvRGEne2GFlbk8+VBv8JhXeSzHJsb79DApGG9t6v7TjPj0fx+s4mq7EneT6QuV7HccDGlJKTJnBNJPMq3kKu9YImKxpO7YvYfpAcoX1RNKPE3CdQWfs5/Qkfzmm+7GYpmt8YxG90aw8W3uaqoc24WxOkVoSovtjszGCY4luUhrB21NCN15KIYRjmf4m5piosTy1d63F3p6m+xMHkDi6mAB8pE2PsYS6H8rqU4QXVfH3pbAcnkV1b2DX6jDMFC3hGwYcWHbZPsDc6kcRwknBaGNN2zEAzKr4DQH3aUgpSWb/QVZfS4X3EoTQMMw0GzvPm3BUl+nGWNf49n1fqHEyadHb5CfwQhsNP3ofWyRHx2fn0XH5fNy9zlFFL7QuPynRc61s7X/trZRijGN5Tr5NCkbATuvVi8nMD1D12yb8rxQjqYwl3P5IDPUZMWVykOgVAwfYBlzrit+OlAa6GSaRfWmXVmTfep8AdniTbI8FKGUWt+MQKryXkNdbKegdRFJ/pC74TZY2NlEd2LuSvu/LTCvhm4zoJTcHyLzrpO72NVT8aRuZhUGabziI1MHl+JpGDqw6GcHbF8RuOEohgCPh26QgnSrtn19AakmIyj9sIfBSMXDBcOJXqlwmftcZLGlYxeKGFThs8/uv9ybv5b3muaxtW9bvZaEqQfyu01CUAEiJEAIh7ARcH2J25f0IYWdl82K29HyJ7bH/DTPK6rYjCKcewu04rLj+5//ymMcncKAIf0nudX9kWqzxTXY9L7k5gPv9MFUPNyF0k65PHkDiqMqi4I3gOTQZsduf2H4/E5kGh9blafZso+W532EPVTLrrM+i2HZMhbdvenR8dh7V922k4o/FSCmxE2uHXfMbarPDpwW5au5N+LQA92/9CfdHhp7ybqfCdxmKsCOxUem9jNbIf+wUX2/nEFga82v+hqr4MWW2mM9EmmhKiJkVdyCEgtd5DKtaDiKRfY6O6A9w2hfRFfsJALnC5mLuDhPS+cHRpofCrs1mfs2TCOGkJfx18voWZlXcgW70sqnrIsvdjWkgfJOe2m7wUf7EFoIvd5Br8NB5yVwKVa4Rp7X7ouBtiL1Oe2Y9s32H0ujZPRlCJyqA7X/7PflUL4V0nNjG9wgtGriEs138Oi+dC/duoOKPWzG8NpKHVQwpfgLB882LOKVxR/Tkg4LHELSVoyk2zqy5kLWJ5SNGc0nl3sHrWFYMUuA+lzLvp8jpm9nQcTam3BHqWlW82NRKhLChSEcxI5sQ/X6+xZfe5/VRzNuxM6ZMsLbtRBy2OWTyK8f0vPyuUxE4UYSdCu8lmDKDplagKH5CnvPoTtw5pnb2Z/brqW4pprb1t60m+HIH0RNqaLluMc6Ep+SiN9VT2bQeY3PyHdJGjNXRFzHlyAdoU4UIW5MrSOsTSys53vv1+upQVDvCBEdZ1ZBlfJsUUBW6Lp5HZq6fqoc24VoXHVSuwR3ipTNv4PWzvkkhf27/9a5sK6oo7qw6lKGSqgsCrg/ic56KwEGsL9CAKQuoihMhFGxqNR7HUQNqGWaUrvid6EaYaPoZYIfomTJLb/I+NnVeMGKUGFMmyOSXM1zSo11JZJ5HksOUeXqS95PMvophpkEaAwIvTGf2W4tvsqLn3Bin5p71iIJJx2fnFdfydoPg7Q3YFCeKUEEKbIoDMcL3oWEW+Ef3I5jSYEP8DU6pvbxYdwIk3nyFtJGg4vBTUTXHsOUWfuDj9HavxekK4YvWEBnmQED/tPfy+dTdupqau9fTeu1ikuyw+k6vXYxXc6ApKp+dcxwPNhd3XU0M8mYOh+okYAtxyczr6c618UCH4DOhV6n0/QvVgWsRqAihYco06fxqsoX3UYSPoPvDSJknk18xaFwdse/Rm7yfBbUvgJAYZpLW8E3Y1CqqAldiU2vZ0nMF4/HYCLjPRhU+IqlHB4Wwz+lNtEe+T1XgS7hsC2iL3kQi+zKGGelzpxPUBG7AZV9Ce/S7ZAtrx9zv/sJ+afFNSvSa/Pj/XgyMabg1Wq7/QMlFb6otvF2xKQ6WVX2SA4MnsqzqwmKo9GEwpI4hdUwMDFkY1Tocju7sVpZH/sb62Kusf/XeEcsqikZl9RJ8/uIUeaTn7dukYLo02q9YiOnUqPnlOpRkoX+z4/WeTRRMg5xR4OmWFf2fg82pdWxLbyBnZEnqcZYEjuC4ig9xUPAY7o8sw2mbhyIcfYmIVBThxes8jJDnPJrD17Gu43TWtB2DbvYgsDGr4lccWP82Qfc5QNGDQwBKn1dFJP1bqgNfRlX8+FynUBf81pifXchzAY1lP6I+dBO1wW8MUUKhvuy/sGu1lHs/jUObQzr/dr8Psd91KhW+z+JzHs/MiumZ4Hy/E75Jid5GHxW/30zlo1tILwrQcv0SCtXDr+eNd7d2bxO8nXFrARo8B+JQPSOWs6suFgaOx6dVcGDwJDRlYu5ReSMNsmhp5YzUuJ9NcG2OfCKCNAYLr2+TghG003H5fNREgZp7N4AhSW4OsCbWzhnP/YhzXvgZv9v6JlD8PBhS586m7/KNlZcSL/TtxgqVnFHMvtYR+xHp/HLy+hZMWfybS2kiZXH6WbxejALjdS7D6zwOm1pFfeg7AGQK79OduJtMfjVbe4q7s+n8CqQ0EaiUez+J13n8mO7dptYghIYQdmxa3RAlTPJ6M4aZQlJAN3oAENgp7hjHEAgkOroxznho+wn71VR3MqKXXu2h9jfrcK+PETm1jvCHG/FtHn4KN17B25+Y6V3KTO/SAddMaSBQRrQWd6bWPZ9Ivp20HuXA4ElIKenJbcV4cyP+w49HiJG/k1e9ez/hZ9dhC4SYf9G/omgDBbg47fXS84kDqHpoE2V/aSZ89gwAYoUMsUJm2LbLHVWIvny6ib51zLt7ZnCx8VGgKDxu+2F4nUfRm3wQVQRw2heRzi9HyizZwqbiMzFzgILfdTrxzLN0xL5HR+x7/f00dX2G+bXP4NBmIqHobwsowo0iXP2JjnalJ3EvLttiVCVIW+SmIcts6PwIPueJpHJvYcgYFd7PURf6FgWjk/UdZ7G198s4bfPoTT484nPeX9lvhG8yopd9x0ndXauwd2bp+tQBJI6qKsnUdn8TvOHYmlzBmtgruFQfx1RdiH3IzYGBKEJlSeiU/t/b0mtZFX0BCcx+rYeGY4ePSSelSW930ZNBj8fIhbtwVTUMKufbpJA4shLn5gSh59rIHuAjSWjUIy4FM49EYmKiy8EpIAtGB7HMU8QyT6EINwvr/o4iPOT1ZtZ3nEbBaGFT10XMrX4UTQkys+IOVjYvGhQqSpKjqetCKnxfIJN/n1TuDRzaHObVPIkinHTGbqMzPjghuSmTbN3JDW4oDDM6wGuk0n8lQmioShCf8wSi6cfHlG5zf2W/mOpOVPSSmwPkX9Wo/9+VaJE87VcuHFH0xjO1nS6ilyxE2Bj/JyDJGkle7XyQ1tSaUesN1Y4pDUypk9TDIz4/IRSq6w4FBG5PJTW9w0c9Aeg5bxa5WjeVDzWhJgqjHm6+q+lmXul+moe23kpHdoc/7lCfM5vWgCp8qIobp20+tYHimltebwJZQEoDKTP9x1V2pWB00B79DtH04wD4XCf1JRbSqA5cPSho6USJpB7HNLNIdFK5fwLgcRyFz3lSSdr3u85gVsXd+Jxjz808lewXvrqjCd9woudsSlDzy7VIu0r7lQvJ17lHFL2xMF0EDyCca+WtnieQmMjiZA0onpM7o+5Lo05Xs0aK9vQ6gvZaPFqQ5eG/YsgCB5WdiVvbIU7DnfvTC1lUzdE/vR7Oxzcxx8Tenqbhh++TWhKi87PzQAicFR0Y8TSO+vL+sqP58g4+1yeYW/0n3PaDEUKQ05tZ21b8PLrsS/E5TyaV+yep3BuAOai9XbFrs1hY+1Ix1p+ZY0vP50lkXxy1XhGVWRV34XUeTUf0h/QkfzOwbbUR3QxjyhRB90doLPshEkln7Gd0J24ftlVFeHA7DiOTf6/fG2VAryLAgQ1vowgHpsyxqmVp/3rnnmba+OpOVPTcqyPU/mINhtdG67WLLdGbALF8Z5/omXi1MhQ0FLS+DZLR1/r+2f0Y6+P/4M3ex9FlniMrz+OYqk8MED0Y/rlqNueANcXh/k6+TQr5WjfhDzXgXRHG824vha5uLm2r4olTrmHZ5h0rPqO5tA3+vEk2d19K3mhBSoOunUJPZfIrCbrPYk7Vg8yreZKd/XOHI69vYXP358kVthHL/IVE9pVR62zHbT8Yr/NYVMVPbfDGwW0bzUUvEMBpOxAh7CjChduxdFDZHQjm1TzNrIo7WVD7HEIMXsaQ6NC3uy+lgRyDwE81+/Qa30RFz7Oil+p7N5Kvc9N+5UIMn21SojfdBA/oC+LpwaX6KMg8BwZPxK64ieTbqHLOGtMmR97MIDERKBTMLDB8cAHXytZxeXyYuk7L84+Qj3ZTf/LH8FFP9OQ6PO+Fiz69l1Rx9devwu12c+vsGznsr98ZsT1VqBjSoHNNhAu/00nDDJWbf1qO0ykwzEiflafidRxFY9n/Ekk9StD9EZy2RQghcNoWYlfrBoSyGnB/9qWYZoacvoFE9lnWto9//S2nb+5LOZkik39/xLI9yXvwOo9FEW46oj8YtpwinDi0mQihIqQNTamgYLQMKGPKFJu6PknAdRbRzJ/HnLJzKimJ8AkhPgj8lOJX2q+klP9TinZHYsKi924v1fdvIDfDS/uVC/G02Yf0t7WsvJFZE3uZ1vRqpIQjKs4l5Cgeq/DaQox1+eSQ8g+xIfY6Fc6Z+G1De2TszFjEL7QuT2SBndiGd4ltXIHUCzQ/91vmf+qroAq6LppD4/ffR7ydxzBNUqkUPZnEgDZ29eU9q+ZTnFx1Lq2ZLRxx0eF0rC6wpUnn6T+mOf9TO47/KMLJ7Kp7UYSToPtsMoV1/V4aBb2N/DABRSu8l1EbvAEQbOm5YtipbdB9Ln7XGXQnftnnyTEQwwyzru1knLYF/et4w6EbnWzsPGfEMgCmzNAVv50K32eJpv48SPS2k86/O2Zf4r2BSQufEEIFfg6cDrQAbwohnpBS7rYAYhMVPe/bPVQ9sJHsbB/tVyzE22obovb+J3pSmoTzbThVLx4tWJI2o/l2DKmjoJIo9PQL36b4W2xIvI7fVslRlRegiuE/YuWORsqrGsfV71jFL+kt3qdQbdj9xc2P4hEXN7ETawi+0M5Hv38nhx13IG/Iwd4WO3N85VkIIah01NI4t56ephhCmDTO3HXqKkHKvlm+pD16C41l/0PB6GJz9+cYbo3P6zwORXEjpYHHccSQwmfXZtFY9kMUxYnfdSIrW4b2p9bNbpK57hHvZ7x0xL5PR+z7JW1zqimFxXcksFFK2QQghPgtcC6wW4Rvwpbe8t6i6M3x0/6FBXhbJi56+4rgbWdV9AXaM+uRwDGVH8dnq5h0mwsDx7Mi/AwuzUute0dYpqbkW4AkpUeI5topd45P2EpFY3om8uzLyMd6CS0cuNYdPrMB7zs96Pe9z6NlEhQb3tkD6+9s9a2Ov82B/kPJmmlO+dbBlB/hwl/r5ohlA/PymjJNU/clhDwXEEn9gVTudda2j34ouTP+M9yOgzHNFOHkb/uvu+0Hc0DVA5iywLaeawE54NC0xcQphfDVAzsvXLQARw1TdlJMeCNjVYTq+zaSneWbdqIHEM61Fa0zoRHPd5dE+Moc9Zxc+7lB1yscM+nObUERakn6GYqxrvf5Zgz+PGz35w2f1UjVw014l/eSPHTkcT6w9adUOGqIFcLoWo7FH5nV987ghOSp3Oukcq+P5Tb6yeSXs7r10EHXK31XoioBFGnid53Mlp4v4nedRG/ywWHb8rvOxK7WEU79bsp2VvcFSrGrO9Qq9qBFHiHEFUKIt4QQb0XCpd/1GU70XOti1Ny9nlyDm/Yrp5/oASwMHIdNceLTKqh2zdktfWxLvs+bPY/T6FnM0RUf44TqS7Crrt3SF4ztbzHSLm/iiEpy9W7KnmxGFMwhz/Zt/0xJJN25dvJmbsD740k+PxGy+pa+c4AFEtmXSWSfpzXyrUG5d2eU38oHGpuYXXEfM8p/Rm3w6zSWDT74bLGDUghfC7DzfKYBGJSYQEp5l5TycCnl4aGy8Xc70odsuCMIjm1Jan69jnyVi/YrF+FtHfqc1/4segBVrtmcWvsFjqn6OJpiJ1HopTW9hsIu/8ijkTWSdGe3DgpMkNKjrI29Qm+umXd6n8Jnq8Cm7Ii2IqVkZeR5Xu64j85M067NTpix/E3sb7cQWfMWRm4XFzVF0HvODGzhHL439kxgToGdKv81VPuvG3AsRBGe4jlAdv58alT5Po8QKgjI5FcN2aZNrSHgPgtF2PC5TkRA0YdX3bvyVu9tlEL43gTmCSFmi2JCz08CT5Sg3X4mInqZ99zU3rUWw2uj/YsL8XRMT9HblbQe4/XuR1gVfZG3eh4fc72skeSVzgdYHv4Lb3Q/hm7ueG6q0KDv+Iqm7LCoTWlgSJ1Ivo32zDrSRoyVkedKdzOM/LfJZqK88/qttLzwezY9NvCArm+TQmZ+gMxsL8Hn2kAf2eorBVX+q6j2X02V/ypq/F8Bink7FtQ+zwFVv2Nu9WM7lZbF83FQ3DAZ1vOjh4LejmGmyBU2Ekn9kWT2NZrDXyvZuPdHJr3GJ6XUhRBfBv5G8TjL3VLKob+eJsBEphPJzQHwSiKn1ZM+MIgRsEPP4HLTTfQAEoXeYhBMjHEFEk3pUUBiSJ1YoYMXO+7huP9n782jI7muO83vRUTuGzKxA7WhgNo3FlncKe4UtVKibEoyJVtry3Ife8bdcts97fa0e3x6uud45rQ9st1t2WqPrZYsS6JWk6JIipS4k1UsFllF1l4Aqgo7kPueEfHmjwASWwLIBFAFFBAfD88pIOK9eAkkbt737r2/2/wobtWPW/VzqP4hxvKXaPPtRAhBrDDA4bEfgpTsDd8HgCK0WcnJV5JC3np9Ui9RjFd4AwhB7L0baPvrUwQOj5C6tXYv6Yep9/PFtnayhTcWTOcQwjn+ASHKTb+dahuaEkFR3Hic+xE4xvX1DM4PfZyI/xES2SfnFCwAnTODD+B27CRXOrlADp2gJfR7eJz7GIj/n+tSh2+CZcnjk1I+ATyxHHNNZbHBDACEIHF3K0DF5OSFjN61ZvDSpSiKUOc1LFJKTsafxxz3HjZ493E8+gyt3u00uDfNO3/Y2UrEuYGRQg8AptQZyp1no28vilCJuNqJuCYDDn3ZdzHHo48j+R5uafw4ydIwTe6tnEm8Qn/uNB3+69ns389Q7jyxYj+bfPsXZRjnCnYE6zbS3HqQ2Ng5mu7+4KzrgYQ3KaQAACAASURBVPMKqZ0h8ht91D07QOrmpopS9ZV6dEzw5c7/QKOzATA4PfAARePinOscTv6/KMIDQmUwYZ3BFfRuUvlfEvTcy0jq76eJiuZKx+mLTU9Edjt20hr6I0rGAJdj/xbQMWWuqhy6gPseGgJfQBEenA3tnB64b8Exa5VrtmRtXqM3hfVg9C6mj/Py8Ld5ceibjObn/sMDSd6c7AfRnTlCX+4kR8f+maIxt0wTWGoqNzR8mB3BO5iIZ51KvMRLw/9YUYy01bMdBRUFlTbvDgKOetq9uyiZeXrSb5I3UpxKPE+iOMRb0afoSR/jyOiPZs1TLZV+Z0IobN/zMW6+8/fpMPdUHigE8XtacY7k8b5buzZdQAuhjJ9nqur8YgltdX9Mvf9RBMqUvhySntEv8valrQzEK0tMTWVzw9cIeN5DxP9xupp/UNNaDTM5LrclcWldbG369qz2mOuFVWv4qj7XG68SWK9GD2A4342JgYnBWKFyZj1YhmBXcOG8smRphAupI6RL0VnXOgIHub/1S5gYSAxyepKsnpx1X717I3e3fp67Wz5Ho3tL+ftOxYMiVBQ0nIoXs5zwa6k7X01CXjdfv+ejfPWPvoBZ76bu2YGa5/hG75/RmznLcPKvK1ZTTKApjYT9j6AoHur9j6Iq4armd2pbcKiTklsTOXxWGdy28vc9zv00h/4VbsfOOefKFo/QO/Y7lvipUPA6r8PjPFDVOtYaq9LwzWf0nj7RiTpQRBkuIdIGCGEZvRllUuvF6AF0Bg6hCScuxccG3+55790cOECjawsCBY8apNW9g4P1HyynnuhmkddGHuNs8lVeHfluRW9OU5y0eqyk5aCzCd8c21On4p6V0qIpTrYGbkQRCmFXG3XOZnYEb6fZ3ckN9R+u+bVLafLm2BM80//XDL36+Lz3zvz9f/a+Q9yxawt3dHRw62fuwHMhhWMgW1OQ42z6OH/X86cEPfexs+0lPI59Fe/TzRglwwpCWOrIC5+v1nkfZkfL0+xsfa4s99Q9/CmK+kVMM89A7D8BoIgAXU3fpTn4u3Q1f5/m0L9h34azbGn4G2b+iSdzT5EuvGSpM8sCBX12LuJ6YNWJFCx0rhf68wEompiNDihJCjf6SW8MlaOKsL6MHkDY1cb9bb+54H1SSpKlYXaG7kRVVJyKF2WGdJQhdUxpIMcDGVKaUKGZ0IHIg+w170URWtWqyxOcS72GKXVG8t0kSkMVFZ2rJVEatpSbpc6ZxMs0M/ssT0qTof6jSNPE1XUrQrVez2AshW6aYELwvk7kn/+c4CvDjH1sS01ruClyD27nLhThoLXuD7gw8ukKd+mcGXgvHufecQGBhXNZQ54HUBQ3UpoEPHeTyj9HyRzg1MAd0+5ThBOEihAKAhfNwd9GCIWA+y7q/Z9BCEE0/U9lZZbukc/hde6joHdXlJmqFU1tIei5j3T+ZYp695LnuxqsOsM3Hy/+WQNOmSH+J5vRLuRR+4toT+WI1PcSv78d06vNq5w8F9ey0auFs8nX6MlYh+A3NTyMW/XPuseletlddzd92ZNs9h1AVeY+A5rv2nz4tTCZUgwQuNVA1eOSxRHSepRm91byZoazyVfwKCEECqpwENDqKwY6Lve8SM+5pwHJhnyCug9ZxvE7L71FIpvHoar8U+wd6vdHCBwZYeyhTXM2I69Ef64HXZqoMkOm8Mac95kyM67LVx0jqb8h4LkLKXWi6W/NeZ9ujnFp7CtE/J9gNPV3NAV/B7djO1KWaKv7t4CC33UbPaNfnBixjIICgu0tj6OKABKDd/tuwpSphYetMKvK8C10rufclELkrK2XvtVNotSI44EcgTdG8ZxNkDlQX3HsfN7eejF6AKOFXsxxYYF4cZA6Z0vF+zb69rDRN0cwYBm4qeFjjBZ6CTqacM9oblQyCyhCnSVukCqN8ero90BCn+sUJTNHsjSCKjR2h+7CpfrLQglSSob6j5LNjLBh8x0Ui6lxnThJsTB5HiklPHnUitYanZLUTY0E3hzD926czP7ZgYq5orunUsf4y3P/gYdCvaQLLy755zNBtvgmJy5X93uIZ39UlppP5Z7H6zqAW9tOa/iPUITriiU0CxxoSmS85WYBVQliGrbhq5pqghlGixP/P4ygZEwG796GdCoUWz3kN/kJHB5FdYSRruke32L63a5VtgVv4a3okzgVL62ebQsPWGakNHkr9hTRwmW2B29jNN/L2dRr1Ls2ciD8IP3ZU5yIP4siVG5t/Dh+x6TxyelWZzCDEplSFLcWKDcEcqn+aek4mTde5mzsSaQ0SMUvsvu6T5PPxZCmSce29+Icl66aSuC8Qmp7CD3gwH9kpKLhm4++XDdp90x15pVBUhhXfT6K27kbl7aVvtgfXaFnFbkU/Tc0BX6LaPb7lOaQ3lptrBrDNx8iZyIFGBtcxP94I97vR2n6xlmStzaT21VHvjNA/RP9ZM3pAY61fK63GBrdm6s6C7xSxIoDjOS7MaTOycTzSGliYjCS7yZZGuZi5rjV4kdKhvPd0wxfg3szje4tJIvD7K67m4Cjnp70MfxaZFYO4kR0WEoTwyzicHrZc12lc7cZqIL0wXpCLw0h8npN293ViU5f7N9d8afEMt8jlvneFX/OcrIqDN983t6zP99E4McDOC7kyd8SQN/sIratDUc4T/3jF9FfGsIRNSh01iM9k2dOttG7MvSm36I3/TYbvXvpCB7ElAZjhUv4tQgeLTjvWCs5WVjncY4GTGmQ0WMIBB41yCbfPk7ER1CESpO7g4weRxUabtWPIlSui7xv2nw7QrdXfE6zu5OtvjES3jwd2x+s6fWlD9ZT9/wgvhNx0odmq7bMl8z8jdhtFXpy2KxGVtzwLbTFjfzVBTIP15P5ZAOuw2k4KvF4E2T2Rbj8u3upfy5J/qAHo24ybcI2eleGnJ7iZOIFQHI69SJ1rlbOpV4lXhwE4I6mT+HRZgcrEsVhooXLtHi6uL3pUdKlUepdG5FAtHCZoLMRp+qh3beLJk8HitDoz57mZPyXgOCGhg9T75rdPnIuhBB0BW+eV7oqPNd2t8OPHnLie2usouFbCEUEMeXsvEbrmg8hHAtGUh1qO5raOG9e4Oy5vbYMVQ2syjy+CUTawGhxUtrpxWh3MXxgK5k9YZSiQeCNEdAUilsj04zeQlxrRi+rJzgefZre9FtVS7rPRboUoy97ary/Re1YAYfJNZxLvkqs0I8x3ns2o8+ufCgYWV4bfYwzyVd4ZeS7eNQATZ6tqIoDTXHQ5OmYFl0WKJyKv8D55OvjSdk6Y/nKfSoWYlG/a0WQ2RfGezoBem3yaZ/f8gfs3fA2nU3fYaZam8d5gD3tR9ndfoSQ5/1zr9mxhx2tz9LZ9E+0hGY3DJqNYGvTP7J3w0m2NHx92pU670fY3XaEHa2/wOPYM/7ygvhdt6EIb02vba2xooZvIW9P+lVKW90E/mYQx2mrpCrfFSR5cxOe0wkaHp9duL3WIrhvjj1OX+4UZ5IvM1ZYnAEAy1t7ZeTbvBt/jtdGHlvUHE7Vw+66u3EIFy7Fz1jxMiYGCioR5/Ra3Ql0swDSas9djcE9m3yVy9l3KZhZQOBQ3LR5565GWApzvVeyu+pQiiae86k5e/DOxK142Rk8gBAqXtcNONTWaddDngcRwoMiXET8vzbnPF7X9VZ6juIl6Ll73md6HHvpavohftetCKEQ9NyHKqz1CuFmU/2f4dCacTs62dTw3xC42NH6c7Y0fp1tLY9TTSe8tcqKGb6FjJ46aL0psw9FKO30oPy0gP+NUZR0Cb3Bjd5ej5qc/oe01oweUE7MllgpHQvV1FaiaOR4efjbGFLHkHrFErOZmNKgYMzeOm3y7eO+ti/R7tuJgoKCyhb/ddzQ8GGUConOPkeYbcFbCDmaORixeleUzDynEy/RnXrTSpCegiI0xPh/nf4bubfli/gd1ZV3VWLq7z0e62aw7wiGUZrz/sB5hVxXEKkKvCcrb0krVXHkzSzdmdPoZol88RQlY3Da9UT2cUyZxZQFxtL/MOfz49nHKeoXMcwUA/H5+1xsavgqPrel3CyljpQlNjf8NxThR0odU+aRUiKlRDeG0dRGNDWMqvhxaR0oFVpFrlZUpW5a6d5SWfEzvkp4HxsFh0L2oQi4FKKb2vFm47h60/iPjFJq8eA5Pkb8I5PlWWs1beX6yAe5kD7KSK6bc6nX6E6/wZ3Nv4GmVNYXrES02DelDlawN3zvvPcXzTwvDX2Lopljs28/O+tm1/d2Bm5EGf/c7AjcUHEeUxrEi4O0+3bTEZiUVn8n/guGcucRKDgU17Qyu67gTWjCAQg6AgdrrgqZi0Ssh+NH/gcAo8Mn2Xvw1+e8V7pU8h0BPOdqi+j+9/P/ByFHhA/7H2dmZUau9A7vXLY8wvnO4gwzyunB6lRTSsYQTm0jSJOSPojL2YHPdYiw72HG0t/gzOD7aQr+S3QjwUjyLzBkgnjmR4S8H2Q09feYsvYP0ZXA7dhJV/MPEUJlIPZ/MZr+2yXPuSKGb8yYXTEwwbO/2EzwpQFifzwu6mxITI9K8o4WlHQJV3+WwLsFEh/YgRGp7pzimvX2AI8WZHfoLn6WseSJTGmS1eMEnQu3Y5wg7GxDUxyUTJMt/uto884vrhkvDqDLIhKTy9mTIAQX02/T5OngQPh9CCFQhUZXcP7WKq+PfJ+UPoYqNN7T/OtlVWar/leClbwybYwqNDqDN1b92qoln7POH02zRD5bQZtvBrmuIOGfXUbJVJ/WIpHES2PMVY4mKcwsKV8SPSNfIuJ/hELpHEHP+9C0JgQK+dJZwGpOfjn6+9PGXIp+hUvRryzfIq4CfvftCDQU4SLs+9i1a/jm4qmLOwh/vRd9swsZ1NAu5HH+zxSBVD9q1mD40a1oapjcjDrwq7HFjRcHORl/nqCzkd2huxDi6p0SCCHoCtzMhdRhTAxeG/0+tzQ+QsBRuVJlJi7Vy10tn6Vk5iuWqc0k7GzFobgwDZ0N3t30pK3ypuFcN9lggpF8L5cyx2nz7KQzeAhD6mRKMVyKjwvpw/RnzxB0NBEvDWF1BpPk9CQOZyMAe+ru4WzSjVPxssG7a8H1pEtRVKEtmC4zF54TfTTu3sfYyCmymWG27/7Y5GudI7qb2xYk8iS4u5Nk99aWzHy1MGWS0ZQV0EjlXySV/wUlY5Bccf52mdcaieyTNAV/GyEVhpN/tfCAKlhVhk+kDQo3+FGiOr5vj+B8NkP83lbSByKEXhwi8vglMnftBHXS6Fytc723o0+RNRKk9TEaXZtp8mxdtrlnEi8O0pM+RrO7k1avVWHRFbyJWHGAscJFDFliIHuGQOjWqudUhYY6bvSKRo53E8+joLCr7s5p/TEAHIqbO5s/g24WcChuxgqXyBpxNOGiO/Uml7MnADibeoWimWMge5rijG1TrNhHi6eL4dwF6l0bphlpl+otqzIvxMX0cU4lXgDghoaHakprmYqiaOw+MD2o4HJpPHjfXs67srz4bs+0a4WNfqQicPekKxq++fL5VgaDZO5nVd6r0BL6Ci7HNgbi/3nVCwuUjL7xLnQqsDzSZavG8D11cQf4IfdgHY7TOdwvJcltDZC62drSJe5swX8ijZIrYfpdC8y2/LhVP3kjjZTgmlFfupxIKTk8+kMMWWI4d4GQs6msStzu2Ums0AdC0OTpWGCmuTmdeJnB3BkECi7Vx47Q7ECTIpSypNQtTY+QKA7hVLy8ODy9tWFf5iQ6s5sWSSRdgZtnJR3XylD+QlkxOpq/vGjDV4nf/1cf4I5buzAF/Ouv/4SXT/WWr0mnQqHdi7snPc8M1yYhz/smlZjVVs4OzS0HFvJ8kI31/w9FvZfzQx/HkCtVySJZLqMHq8jwYUpQBNKnUrzeT9KsRzonPbuGn1qimFON3tWM4h6s/yD92dP4HRFCzivbwUpMCbZP/XebbwcR9wYUoeJUFheRG81fpD93svz1TG9vJlJKK13F1Y4hdZyKm5JZRI4bI011ohuThs+l+PCoAXaH76kYjS0aORShVh2c6QwcIl4cQBUO2nzzp7VIKTFkCVU4ZgVFKqm2NDcFcTg0ikWd5rrZRwCFzX4Ch0es92YNLHcFh1PbgtuxnVTul8gKHzK1YsoMAoHEwDDnFxRorfsDVMWHS9tC0PvANVeaNherwvA9dXHHrMQavX7yD9vZn8Xz9gDJ908eyl/t1BWH4lq0ZlwtCCG4qeFhLmVO0OTpmFUJMVPNpFa600eR40nIAa2RLf6D5WuXMu/Qnz1NwUgTdrWxyXeAw6Pfx5RmuXri9qZHp3iidfxi8P8DQEHlQOR9NM9zBDCQPcvx2NMw/hpDjubya56KlNJqSo5KvWsjD7R9ecHXJaXk6Ng/M1LoJeJs48aGhxeMCP/ff/4kX/lfHqS/P8bjR2Y33ils8BF6cQjHWJ60sjJ1u051I9tbngQgWzjKhZFHqx7rduygs+mfAJULI58un/2l8r/kcvTf0xz6XdyO7fjd7yGdf6HiHKn8L9HUZkCSLVRfSbLaWXHDV+yXeH80htQERpMDfYubZHq8VEhKEAJfL2Ru3YQRvnINqlcTQWcje5z3LNt8UsqyEQg5msuJ0BkjVhYiPRF7lsvZyeZ4hVyGopFHl9YHzPnkYQq+LNlSggvpwwAcrP8Ae+ru4XTyRcLONpqmSMxPJVro442xn4wLnJog4bWRx5CYqDi4pWl6oKYn/SbnUq8hgd2hO9lQhURWSRYYKfQCklhxgIKZWTCQ09M7yu98xdq6FysEOAobrA8Z56UMpcar994Two1T24THsQef6xAAquLD45xfXXsm9f5PoyoRhBA0Br7IxbHfmfIQiaY2oCpe2uv+I6cHK6c49cX+iFjmMUrG4KzcRACP8zp8rhuJZ3+CXuH6amXFDd/x33IibjLQ4jpqVEd5tohvp2LJAgmBGiugN/igafJNvCYTlStgSoNooQ+vVod3kRHNU4kX6Um/ScTZzqGGj9Lu2zXu9Znj+XKWmslUowfWiUqTewtjhYuYGESLl4kV+8e9RctjvJx5lw2+PdzV/Jl5o9wXUm+Uy9om57dSPgxK9GdPsiM0qSqcLI2O5x0KUqW52ipOxyFc1DlbSBSHCDjqcSkLpzrlslEG+w4TCncgduyddb3Y4kEq4BzMkalqFUtHER52tD6LpjYhUJGyRMkYxjRT9MUWbkY0lVT+l0R8n0BKSOam9zPOF09ZMl9mZkFR0uwcNcMOtY2upu8AKg3+z8xShl7NrKjhe/YXm/HXD5P5dSuAofbmMV8SuM8mMR0K+c4AjT8ZIntoA9K18FLXktEDOBZ9suyd3d70azW1XpzI2J9IRYmXhkiXxgg6G9EUJyUzT9HMk9UTeNQgXjVE3rAO8rf4r6fRvZmwq5WiLHAu+SoSE4k5fuYoECgM5y8wlD9P2NnOzY1WioghdaKFyziEh5CziXhxsKzAIlDY5NvPxczb5YAFCBrcm6etfVvwZtJ6FAVlWuLzfAghuLnhY+SMNG7VX9EQzzzne/vI35DPxVGUF+na/RXc4Rm5kZpCqd6Nc7Byou+ViOw6tQ6rz65wjnvqDvKl0/SMfr7muZK5Zzg9+AAClYJ+Ydq1XOkEZ4Y+hFNtJ5V/flFrVZU6ABTFiUZ1qVWrhRU1fGZEQ4nquJ9LkL8nRMJsRtlfQpiS0AuDaEqI3P7WaUZvrVZoVCJa6Bs/rNdIl8aqNnyp0iivjTyGiUnA0UhGj+EQrvL4iTIxIQSGLCGE4LamTxIt9OFUvfi1cDn40ObZTk/6KCUzj0vxEXQ0sj/8Xnozb3Mu9Spgpa5MdO56bfgxkvowAA2uzaT1MfJGGgWVPXX30uLtIq2PkSyNssm3nw2+XbO2pF4txO1Nn6z55yWEUpNnbOgFJrxX/7kMeoW86VKzB+fw1atwyJfOkC2ewOe6kXzpLEX9In2xf7/o+Yp675zXCqUzFEpnFj13vvQuQ8mvEvTcz1Div9Y0tjHwW4R9H2U4+ZfEsz9e9BoWy4oZvqcu7oA6SH+hGc/PYihxnex2H6bPQfL2ZjynEzj7khQ3T0YG18sWF2Awd658vqagYSLJ6amKsk8ZPU7eSBFxbkAIweXMu+WxeT3FwcgHCTtbysbs+voPcT51mEb3FgIO6zxVU5yMFS5xKXMCVWjc3vwobtWPRwtwT8sXxrXzoggUzqcPlz1JsLaZIKxmRuNGD2C0cBG/FgHSSEz8jjCq0DjU8JFp68/qCaKFfhrdm3Gp07eoBSPLYO4sdc6WZY+m77n+M/Sef5ZIw3YCwXYqddUtNbjxnE7M6uJ35dA5P/wrWDlrszvcTcXt2IWURQr6+auyskoMJ7/KcPKrNY1xqptoCf1rFMUSUohnn2A5U1WqYUmGTwjxCPDHwC7gJinlkVrnKO7zIgUoz5aof6eH/LYQ+c1+vGeTxK7bUtUca83oAeNekoKJQUnmORZ9AhDsDt3FJv9k6UqqNMorI99FIGj1bGNv+D4a3Vu4mHkbiaQk8wxmz9A4rlJcMLKkS1F2hG4n6Gic9syB3FlMDASCeHGQBtcm3oo+Sc5I0+TuoCdzDCSY429SgcoW/wE2+w8ghOBc8nVUHBhY53kbvLunnNFZ53UzjVfJzPPS8D8ipcSpesbPCyejsa+NPEbOSCGE4D1Nn1p09UYlQnWb2X/D5+a9p1TvQimZqKm5hQ1m0uhqpT38J6TzL5PI/XSRq5vf6EV8v0Z72Drz6xn9LVL5ny/yOVcfQyaRGJhmHkMmudpGD5bu8Z0APgb8dS2DkkU35dMURVDa7yNnuPFcSBH65SDu7hTpmzdhhCZTWtbTFhdgg3cP8eIgscIABXMiiVbSlz1ZNnyG1BnMnh+XcDeJFvoBaHBvojNwE+dTR6zG01O8xNdGvlc+y/OoATTFycH6D+JW/XT4D3I6+TJOxUvEtYH+7ClGC5eQmOQyKcxxoQMFS5fPobjpDNyIpjiJF4c5l5rsIHZPy+dxqT6Ojj2OKCkIoVTMGcwZ6fFAhiRvpJBIK8ds3MMqmBkkBgKNopnDw/IZvoUInFfQI9aatWih6prdf7H1Dwk76on4PsHZoW7ypdmpMktem+ceFMWDlAZ+1y3XluEz45wdegi/61aSuadWZA1LMnxSypMwOw+rVtLdIWvbe72L9PUNBM4wrSxtPtaitwegKQ6ui7yPnJ7i8OgPyBoJQJTz7hLFYV4ffWyK6sp0KfbOwI14tRCmNGmfIkqQNzLjgQVBxoiDIehJH2Nn6A46Atdb3hsKQghcin8y+iqL41tuHROdsKOdGxo+VN4+96Ymt74KGg7FSv/YH36A3vTbeLQATe7ZOX59mXfL/252d6EIhZF8D2+OPYGqONgVupPezNs0ujYTdDRhSoO3Y0+TLI6wJ3w39a6NC/4szyZfYzB3lq3+G2g/wbzKzDPRQ9br0xKlqlOHVVQsrTuJYLZU13IwnPxLfK4bkbLAWOabC9xtrWU1sdTzxaWy4uksFVHtTmkTeLQAd7b8Rtmrm2i7OJA9Pc3oCRQaphgBIURFFZb94fdyLvUaTsVtScYLQUCbjMhN1dSbKYIQcNSTKA0BECv1cWT0Rxxq+Aia4sSrWf1tJZKt/uvL+YGa4qQzeGjO12edRUos0VEXh0d/RLRw2dJtMU0KZmZaoGMo111uWHQi9nPuavnsvD+/jB6nO/UGJgYn4j+ndQFlmpkYISvlR01W/x782+7/wj1NH6bB/CG50jsLD1gEueJbvNt3cMH7wt5fZWP9n1LU+zg79BCGGb0i65kLVYQQwolujlzV5y7Egm6VEOIZIcSJCv9/ZKGxM+b5khDiiBDiiJ6Y1CObqXBbS0PwtertTaU/e4ZXR75HX/ZU2egNZs/Rk5lQ4BC4FT976+6tqsF3i7eTO5ofZVfoLtyqH59aR6N7C/HiIC8OfYtj0SfLBtXrCBF2Wt6RQ3hodndNK6FL6qMM5c4jpbTqmDERCIYLPVW/vh3B29GEEwH0ZU8RK/SVvUyBoGjkpomverWQleYxrs68EA7FjRCWYKpT8ZZbUlaL4XMgBWjJ6s/4BvK9fOviXxDLfKemZ10JmkP/K0JoaGojQU91whDLhcd5HbvbX2dX+yvUeR++qs9eiAU9Pinl/cvxICnl14CvAXi3tVXtd69nb083ixyPPY3EJFEcYqxwmUb3Zs4nDzOxdeny30hXaH5dvEqcSb5M1kggULiYOcFg7ixpfYysnmDIfa4s935Tw8P8fOBrlGSOc6lXuaXhVzmfPsJY4SISCDgbGCtcYiBnbVskJqnSwnp3EzhVDyYmEoky/qpUoeFXG0jpI1zMHCdeHOTWpo8DEHQ0oikuimaWVClKuhSd1oZy1vyKm1sbP0Gs2Eeju2PeY5lKElUoAtOroWSv/gH8chDPPkFj4HOASaZw+Ko+O+i5ByGsD56I/xHi2R9c1efPx4puddPdIeq/30Nho4/0jY22tzcDRaioQsOQJSQmA7nTDOXOM/W8xqtVL8ueLsVIloZodHfgd0SIFi8jpSRrxHGrfrJ6AgR41Jn5gpPGwqG6ORh5P9FCH24tgE+rI8VYeUUCwc5QbRn8++ru42zyVRrdm9ng3UfOsAIIb8WetCTwzZl1E9bThBDjoqbz43eElyRfb3g11Ez1Ht9qYjDxn4llvotujmGYlRJ2rhzx7OM0Br6IwM1I8usLD7iKLDWd5WHgq0Aj8LgQ4piUsupGpo6hHKEXBonfX/mweT17e2AZvlsaH2E4f4Hu1DFKMgcCHMJNwcygoBJyTqakpEqjmNKYljJiSoNTiRdIlcZIFIes2mf1KLc1fRKPFuLd+C/oz54CBH41TEfgBsKuyUY5E6IJFzPHaXJvKSdB17snzxMDjnpuaniYZGmEFk8X78Sf5VzyNbYFb52WejMXrd7ttHq3T85HBCklG717iRcHp5WzAdxQBfN9QwAAIABJREFU/xAXUkeod20i6GycOd2yY3pUlPzCBvbKouJx7KSgd9fcRrKgn7tCa1rguaUznLh8wCq9WwZVmeVkqVHdHwCL8l/T3SEanzuP1ASJO1tsb28O/I4IfkeERncHPamjRFwbCbta6cucJOxqwzfuyQzlLvBWzBKi3BG8jc3+A4CVCH058+5kiZiEtB7lZOIF2jw7mfQeJWkjSk/6KO0z5J+Czkb2OisXsadLUeLFARrdHYRdrUQLfYwVLmPIEqeTL7HJv490KUbOSFLv2lgOelQiURzinfgv8GsR9obvrdjrAyDkbOJg/Qeq/AkuHdOtIgq1tZpcbrY2fQuv8zoMM8HpgbuumX4ZoCNXIE9vIVZsq6smiwQOj5K8pQkj4IDh6dfXu7c3k4Cjnn2RB8pfbwvdMu16tNBXzrOLFvrKhs+peKb1tbA+fQ0uZU5YB/7CS3GKB6EtoM83lYKR5eXhb5eTnt/T/Bt4Nat+UxUOgo4mkqURXh35HgJBs7uT/VNew0yOx35OWh8jrUdpyG1asDfI1UI6VdT0SnosAr/rFoRQEFj6fPnSyQVH2czNirSXNAoqwZeHEYYkcbft7VVCSklP6k1OxJ4tJxzPxdnkq/RmjlmKyoqPzsBk0WmDexN15a2vIOhoQEG1JAMUdbyxj3WGF9SaOBip3pMqmrmyUZVILqffwa36eE/zp7ku8n4ONTxEerxyw5Al4sWBeefzakErOVpaydVXilrfQ1ITiBqbiy8vkpHU3yKlSabwBvkVzH9bK6yMxyclwZeHyOyuo9TowT2jzeta8/ZG8xd5M/o4DuHm5sZfqarsqid9jNPJlwBJWo9yS+OvznsvWGeC+yMPzDr32ld3P8eiP0URGgciD9KfPU1eT9OXOYkiVDr9h8gZKToDN5bl5hdCSolfixBxthMtXgYEYXcbYMn0TwgPNLm3EnK8Q0aPs6vuznnn3B9+kIHcabxaHWFXW1XrmEqiOMzx2DN4tSD7ww+iVZHeUw1SVRDGyiYAD8T/hIH4n6zoGtYSK2L41JyBliwx/J714e2dS72OIXVMmWEgd5atc/ShnUBKydnkq0ycv8kFIpeN7i0M5y6MN+NWKRp5QJaNmM8R5vbmSeXeOmcLR1I/Kn99If0GAoWRQg/3tHy+nMRcNHKzSs2klLwVe4rB3Bma3Z3c2PBRkqURKwWlQlqJpji5ufFX5l2/bhbpTh/FIVzjdb+L24i8G//FeEpOnP7caTb5ZmvsLQapClhhw2ezvKyI4VPSJUoNLnI7QgRmNHhazd6eKQ0uZd5BFRrt3l1Vl+o1u7eSLFmZ62FnlZ5MucpIsKvurnlvPRB+kLR/jDfGfsLro9/HKpVS2FN3z7Rm3RNMeIjW7KKstSdNE0OWUIRalomXWLl8E5HekplnKGf1bR3Od1MwM4Rq6PFbiZOJ5+nPnh7ffmts8i0cCa6ETwuT0q2ttW9WSs4SkJIa855tVjkrY/gKJsnbmkGp/t20Gry9M8lXuJh+GxDossSW8QDCTApGhv7saULOZiKudjoC19Pg3owmnBVlpWYihOBg+AOcSrxAyNlMyDHbsHSnjtKXPUWH/yDtvl2MFS6TNyfPAq1m4O9WNHxt3p3jZWGSvXX3UjRzXMqcYJN/f7kaoi97shwJfmPsJ9zV8hkciguH4sav1ZPR43i0AM4qlI4XYkKkAASGufgI4N7wvTTkNuFW/URc1dfj2iwXAk1tQjeGWW21wTNZsahu8qbZCcur2dsDa+tnlVMJisbcuVSvj/6QrB5HoHBb0yetBFotQs5IYki9XHoGVnvGc6nXaXZvZUfojrIXeTn7DhkjTi6XJOJqn2bAcnqKs8lXy/WnLd5ts5J8J9SOK9Hm3U7Y2YqCikuzDNcW/0GyeoJzycPk9AStni5GC5aIpSkNxgqXaPF0IYTg1qaPk9aj+LTwvOkp1bI9cCtFI4tXDZUbOvWm32Iod4GtgRtoGJfUWghFqFckEiwkNX1Ir08EXc0/wOPcR7ZwlPPDjyBw4HR0UCx1I1ldCeArYvhK9S5MvwOGqrt/NXh7YKmf6LKIKrR5z+mKpmUgFaFQMvMAHI89w2DuLA7FzR3Nn8KhuJBSciL+LBKTi5kTtPt2E3DUW13G8lbjHBMD3ZyeSqEpTqv+VIKqOFBQcIjJutUdwTvY6NszZwvHodwFjkV/ilPxcGvTx3Grfo5Ff8pwvrtcJ5sx4mzw7qE/ewpVqNQ5W8rjFaHO0vJbCm9E/5m8kSRZGmG7vJ2inuB04iVMDOLRQR5o/fKSFYCWgtBN65zPZk40tRmPcx+KcOJzHUJVwmxt+iZurYuC3suZwQeBlc2FnMqKGD7Tq9UU1FgtuFQv19d/cMH7Dkbez5nkK9Q7N5QNxlD+nGXEZJFkaYR6l6WW7FGD5I30uAyU5X1JzLLYJ0DDjO5lDsXFrY0fZ6xwiSb3VoRQSOqT6hd5IzVv39rzqcNITIpmjsHcObb4r2M4f6HcdhKss789dffQ4T+IS/VV3Qe3FqSUxIsDZHRLMUQRGgUjbW23hQApLAGDcaM3lLvAO/Fn8Wlhbqh/aNmitgshdInUanu/Lmdf3WsB3RgiWziKz3WIdN567R7HLoTQcDk60ZQGdHN4gVmuHqtGlmqube5q8fZqIeJqn5V+stG3j570Mdyqv9xPFuCWxl9lpNBDnbO1HIVVhEqH7xC92WO4FT9vjj1OV/BmWr3byuP8jggeNYAyvm3eGriBWKEfRahsmtL/t2BkGM1fJOxqL/ejaPZ0Wvl1QhByNHMu+ToBrZGkPoyCRrO7izbfDiRmuTLkSnAq8QKXs+8gUFCFkxZPJ36tHiEEN9Z/hGihb1op26nECxTNHHqxxHC+m7Yp164komhguq69D+qri+T88COoSrhcExzP/pSw78Okcs+uKqMHq8jwrXV2hu5gW+BmK+VkyrbNqXpo9+6adf9YsRcpTbJGHIC3Y0+Vz9gAziVf51zqdTxqgNuaPknQ0cg9rdM7cUlp8vzgNzDQUVG5p/ULaIqTDd7dNLqs/hZnk6/Rlz1ZPruUmFb3tMI5/FqYWxs/ccW2maOFSxhSR0FjR+g2Nk7pnxt2tc3K5atztlDM55DIWVqBVxIlb2B67T+VapgqhHBx7F+O9/Jd6Trn2axMHt/qqle+alSjlzfBxDkhWIEKl+qbZoB6M28BkqKZI1bop8nTQdHMEy8MUOdswal6iBX6y/0vDHSGcz2cSb5E3szgVDzc0fToeL9bK6I6MbtBESQkSyMYsoQmln+bC7A9eCvHY0/jUQM0ezoXvH9f+AGihct4tCC+8dK4q4GSN9DD1Zfy2Uxl9Rk9WCUe31ra5i4X10Xez+nEy/i0OgJaA83e6YahxbONvsy7qEIj5GzGlCYvD/8jJbOAKhzc3fJZNMU1ropsGdC3408xkWagmwXixQF2he5EQUFKS3JKxUGs2E+s1IdPC3MlE9ga3ZstlRg1WJVXqQil6gjvcqJkDQzb41tT2L/NJXAxfZzezDHavLvoDMwtr74Y6pwt5SbdldgduostvoOM5ns5nzrMRt8eCkYGicSUBiUzT9DZyIHIg7wV/dm48ZsMXqiKo3yuGHQ2cTrx0nhwQ5YrN7J6gu70G2wLTgoi5I00scIA9a4NVZe3VUI3S7w0/C0KRoYG9+aqgkYrgpSo2RKm3/5TWUus+G9ztefuzYVhljiZ+CUSybnk67R7d85qjH0lEUKQMxKcTr2EKQ0SxUE6/NdzKfsO7d5duFQfAC2eLvKhDKcSz0+MZLNvPztCt5cNXF/21KRsFVbenhj/T5nyFjHMEi8N/yOm1NGEi7tbPrvo8rKMHqVgZjExGM53LzxghVByBsK0JOht1g4rbvjmYrVvcxWh4lDc6GYRRahX7BxsPqweFxP/kmwP3cb20G2z7tviP8BI/gKxwgAIQat3+7SmQh3+g7wde7p8yieEoM2zC48WYIv/uvJ9JVlAN4tWuo00MKRe1eseznWT0WNs8O0p1/0GHA2WenNplI3ePQvMsLzU0mVtosmQEbQN31pi1Rq+1Y4QVlXGSL6HetfGJeW5FY0cw/lu6pwt0wr9rbrYC4ScTQQcDbPGNbg20xW4hVRplCZPB6cTL9Hi2VaxdvZg5IP0ZU/hd4SJFQZ4O/o0m/z7qXM2Ey8OcWPDRwk7W8kaSRzCVXEbO9F793L2XXxaeDylZP5KiWihj2OxJ5HSZLRwkRsbPgpYHxy3NX7SCp5cgRzBxTCr3wZWW0mw2kxW01PX5trANnxLwK362TiPAoiUkt7MW8SLg3QFbqqoXiKl5Pmhf0CXRQQKd7V8prxlfn3kB2T0OELA7U2fKufhTSCEoCNwEN0s8uzg1zGlzsXMce5t/SKq0CgaOd6KPokui+yPPMhm/36KRo4joz9GYnI68SJWCovBpewJ7m354oLR0q2BQ/Rk3rICIMWBBetii2YWAZiYFGaU+QkhZnmMhtTJG2m8amhFqzUm0BKWx6eHnGirTD7dZvGsaFbmWo/mRot9nEm+wmDuLEejj1e8J1EaGu8ta21YpxqHnJEsV3AU5hEjNTGR0orcmtJASiuI0Zt5m2ixj0RpmBeHvkm8OIiqOFCFAwUVTTgoBzykpJrC8uF8T1npmfFAynw0uTvZ4N1DxLmBA5H3znuvbhZ5YegbvDTe5nKlSXWaaNECUoBeN9sbfO+m0yuwqpVDU5tpCf0+Ie+HVnopS8b2+K4gCmrFf0/FrQbKKSdO4ZlWA7sv/ABnki9T79pInbO14nhTmuWorUcNsqvuznIpl+W9WfpWEpPzycPc0PBhbmv6JGOFizS4NpPSR7mceYcN89T2TiXkaERBw8Qg6GigfkoT84o/A6HMK0CaN9IM5s4SdrZhSpOSmR8PeFxYcC1XAy1awAg6oYaStbVarral4W/xOvciZZELxtBVb1e5nNiG7woSdrWyt+5eksVhNk8JEkxlQqo9URym0b152vau2bOVZs/WeZ+RKo0QK1gecs5I0ejaUr7W5t1BVk9yPvU6IMo5cF4tiFeztugeLUCTu2PeZ0gp0WUBh+LG5whzZ8uvk9NT1DlblrwdfXXkuxSMLEIo3N70KF61jpQ+umhNvuXGMZqnVG8nLwOoihdQsMRqli5HtpKsmOG7VtNYaqXNu2NaACBTiiGEUm7TCODVQtO+roXu1JvlVJSgo3GWIeoK3kirpwtD6rMk6aWUvBN/luF8D12Bmyq2gjSkzivD3yGtR2nz7GB/5IFp0vJLZULqS0iBKXVua/okJsY06a6VxDGSJ7v76lWJrGZ6Rr5MS93vkSu8TSr/y5VezpJYHe+uKayV871K9GVO8k78OQCuq3//gp5WNcRLVgMfBZUtvspe5VxCA6nSKP25M5hS52TieTb69s4ynOlSlKyRACT9udPsk/cva9Dhusj7OZ96nSZPZ7n+Vl0lb0slq6OlSpSaFp+ovZYo6GfpHf3NlV7GsrA63mHrhJFCT9k7G81frNnwTaS9hJ2tOBQ3qVIUpAIIfFqYJk9t87lVPwoKQjjmLBvzOyK4VT85PTkugbW8kdYmT0fN614KteTwOQet3rXFFo+dyrLGsA3fVWSL/yCj+UsIBO3e2ZLwC/HKyHesqK8ApJxWbeFz1NWcD+dUPdze9CiJ0hANrso1sKrQuKPpUYpmDpfiq3nN1wqVcvicA1aEvdjqxU1+2rX1FtFdaywpnUUI8adCiFNCiLeFED8QQlR1GKLmK6dNrOVtLlj1tzc1PoyJyWsj32U0f7HqsVJK8kYaEx0pzWmiodYNi/PEPFqAFk/XvEZTESpu1b8q8uquFqlOE2d/FsOtooer/0BZqxHdtcZS8/ieBvZKKfcDZ4D/belLWtv0Z09jyCImxri0VHUIIdhbdy9eNcQG7x6cigfL9bOMUUaP17yWWGGA86nDZHV7G1cJ1+UMxXavpQZts6ZY0lZXSvnUlC9fBebuem0DQJO7Y7xTG7R6amuM0+7bRbvPEi3dLe8iVRrjtdHvIaVJu29nTXPljTSHx36IKQ0upo/PEjFd95gSZ3+W5G1La51pszpZzjO+zwP/tIzzrUkirnbubvkcJsaSUkKEEASdDdzd8jl0szhn28oziZetRkbendMSiXWzWK7WKMn1UYpVa2BDKZkUNqzdc831zIKGTwjxDNBS4dIfSil/NH7PHwI68M155vkS8CUAl3t950UtRcduJlav28kEWyklydIwqnAyku/hQvoNAC5mjtMRuL5sbBPFYQKOBiSS7cFbq3qWYZY4EX+OrB5nb929BJyzhROuRSoFNly9VolgYbN/VkTXDmxc+yxo+KSU9893XQjxGeBDwH1yoki08jxfA74GEAhtmHXfWg9sXC3OJl+lJ3OsrKkHIFBxKK7xc0FIFkd4J/EcptRxq/6qVY27U8cYyFl/9K+MfIf7235zmrzVWiHVadJ4OI3hVSk1unFRXbK9Hdi4dljSVlcI8T7gD4C7pJRzd9i2uWqMFHrLIgISiUChzbuDHcHb5jBS1R/cK8rkeKvfb3FZvdfVhPtCkvyWgB3YWKMsNar7F0AAeFoIcUwI8d+XYU0rhqVkPGSdf12jbA/egiaceNQgYWcbEdcGooXLHBn7MXk9RX/2FBk9xu7g3Wzw7uZQ/UNVz93hP0ijawuqcLDVf+OaNXpKuoRzOE9+a+VzU5trn6VGdbuWayGrgcOjPyyfj93Z/OurRiCzFhrdW7i/bbKs6Mjoj8gZSfJGirdiT5MoDoGAHcHb2Bu+r6a5hRDc0PDh5V7yVWGuwEal8z3PhRQA+a1Bu2JjjWJ3SR5HSkmsOIAhdXRZvCZz28xxTb6p1DlbUIWGECoKAhMDKQ1yenIFVrj6SXWaeM4kMJ0K+U2zI7pzBTbs871rC7tkbRwhBFv919OdPkrY2Yp/mRpWp0qjvDn2BKri5Ib6D12xhkQn4y/QmzlGyGF1Z5s4z+sM3ESdsxVNceJW/RyPPoMQCluXuSvcWsJzOkGuM1iTBp/NtYVt+KYwV7OepXAm+aqlbmIILqWPsy1UXepIrVwcrwJJ66OkSqOEnM2AZdCnRm1vbPzoFXn+aqaW/D0tWsA5kid5e/MVXJHNSrMqPtKudirLQPYMzw38D45Fn6y4PayElJLB3FmGc93MzNoZzl3gXPJ1CkZm1rg6ZzOq0FCESrBCE6DlosG1eVxO3jXeCNxmISqd73nfjQGQ3VVn5++tYdalx/dO/BfossBIvptYsW9B+XSAc8nX6Mm8icRq5r3BZ6mrxIuDHIv9DCmt/rC3NX1i2rit/kOEHM1oipM6Z6U88OVhb/g+snqCoKMBVam+FaIpTauDrp22QarTpOXZOKV6F6UmO39vLbMuDV/AUU+yNAyAV61O+ThjxDGkjkCQnSIIoJvF8S5iEt2cXfo1c6t5JRjJ9/LmmNXM6Pr6D1X9vOF8N2+OPYEmHNzS+MicgqXrBVE08JxJkrql0c7fW+OsS8N3qP4hRgq9BBwNeGa0bJyL7cFbyRspVDS2+A+Wv1/v2kiH/3rixSG2X6Hzu4UYyJ4pa/MNZM/UUInxJhKTkiwwmDtHp+PGK7nMFaGmNJbTCZSSSWZvxE5jWeOsS8OnKg5aPLWlIHq1ELc0PjLr+0IIuoI3L9fSFsUG324Gc+fK/66WVs92EsVBQFDvXni7v5ZJdZo0fiuG4VbJdQXwk5p23U5jWVusS8O32rmUOcFY4TJb/TfMahBUiYirnfva/gUCUVPt7Cb/Xhrdm1CFY81WYVSNYeI7ESO7Jwzqqoj52VxB7N/wKiNRHOZk/AUGc2d5Y+zHVY+biBzXikcLrlmjV9M290wSNauTvs7e5q4HbMO3ylCEUtYNqNWQxQr99KSPWX05bKom1Wnif3MM06WS2zlbMs1OY1l72FvdVUbA0cD+8ANEC/1s9u+vely6FOPw2I+Q0uRy5l3uaH70Cq5y9VNL0rIomvjejpI+EEE6qvcF7PO9axfb8K1CWjxdNQdfSmZuPK3GpGDaHt9cVExaPhFFzRukDzXY29x1gr3VXSPUOVvZ5DtAyNHMdZH3rfRyrhlSnSaBw6PodU5yXbNTm+xo7trE9vjWCEIIdixznfG1Si1BDTVexHsqTvz+NlDspOX1gu3x2axbLG9vBCEhdVOjXZu7jlh3hm8k38ulzAmMcXn2lWQge5aT8eevSe2/1UotQQ1MSfDVYXJbA5Qaq0/psbe51z7raqs7ku/lzegTICFa6ONA5MEVW0uyOMLx2DOY6Izke7iz5TdWbC3rgcq5ewkcYwWiH9hoBzXWGevK48sbKZASE52csbIKxCZGOV9vos7WZmnU4u2lOk1CLw5h+DXSByKzrtvb3LXNuvL42rw7GSv0kTeS7Km7d0XXUudsYWfwDqLFy3QG1p44wGqikrenjebxvhMjfn97TUrL9jZ3bbCuDJ8qNK5bwe3tTDb597GJfSu9jHVHqtOk/geDIASJ25vtoMY6ZF1tdW3WLrWksIi8TuC1EdIHIhh11XfSs729tYNt+GzWFalOk+ArI6h5g8Q9rXZQY51iGz6ba56aUlgMk9AvB8h1Bihsmt3xzt7mrg9sw2ezZpm5zU11mgSOjOKIF4nf11aTt2dvc9cWSzJ8Qog/EUK8LYQ4JoR4SgjRtlwLs7Gphtq8PUnd0/0UNvjI7rLlp9YzS/X4/lRKuV9KeR3wz8D/vphJanrz2thUQSVvz//mGM7RPLH3tuPfWn0ep+3trT2WZPiklFPfPT5AznWvjc1yU0skF0MS/tllCq1eMntnd5Ozvb31xZLz+IQQ/wn4DSAB3LPkFdnYVEGtVRr+10dxjuQZ/Px2/J22t7feWdDjE0I8I4Q4UeH/jwBIKf9QSrkR+Cbw2/PM8yUhxBEhxJFSMbN8r8DGZgoVvT3dJPKzyxQ2eMnss709myo8Pinl/VXO9S3gceA/zDHP14CvAQRCG+wtsc2iqdXbC74wjGOswMCXdthnezbA0qO626Z8+RBwamnLsbFZPHNVaUSevExuW9CO5NqUWeoZ338RQuwATKAX+PJiJ8rtbcdzom+Jy7FZ69Tq7UUe70fN6Ix9eJPt7dmUWZLhk1L+ynItxMZmIeYzehUVWKIFQs8NkLqhgcImPw5sMQIbC7tyw2ZNkuo0ifzkIgiIfqg2oVHb21v72IbP5pqgVm/PfTZB4M0x4ve2oYdds67b3t76ZlUZPruCw6YStRq91Badxsd6KEVcxO9rt709m1msKsNnY7NUUp0moeeHcA7mGP3YZnw7UrPusb09G9vw2axqag5oxApEfnqJzO46sntqS1a2vb31g234bFYtNW9xtxo0fK8bgNFf2WKnr9jMyYoYPsM9d8d6+5zPZjGkOk38R8fwvRMn+oGN6PXuWffYW1ybCWyPz2ZVUqu3p6aKNHy/h/xmP4k7W+yAhs282IbPZtVR8xa306Thez0oeYPhX9taUX3F9vZsprJihq+iisY49nZ3/VLr7z7VaeI7Oor/rSjR922g1OKddY8d0LCZie3x2awaFjJ6Fbe4sQKN3+0mv9lP/N7a+mjYrF9WreGzvT6bqVTc4nYYNH/rPMKQDH26C39XbVtc29tbv6yo4Ztvu2uzvljMuV7ds/14ziYZ/dgW9Mbaori20VvfrFqPz2b9sBij5+pOEXniEunrIqRubrS3uDY1saoNn73dXfss5nesZEo0//1Z9DoXIx/fWjFR2fb2bOZjxQ2fvd1dvywmmJHqMGj6n+fRUiWGPrsN757Z/Vtso2ezECtu+BbC9vrWJosyep0mdc/04TsZZ/ThzRQ2+WfdY+fr2VTDqjB8tte3vlis0fOcjBP56WVSN9STvL255nM929uzmWBVGL6FsL2+tcNijB6AYzhH89+fpdjqtc/1bJbMNWH4wDZ+a4HFGr1MW5GWvz0NqmDwC9vx7UzPusfe4trUwsqos8xWAre3u2ucxX5wpbYYNP3DORyjBQY/tx33ocKsexYyera3ZzOTa8bjA9vru1ap5vc2p77eY934TsYZ+dUt5LuCNT/bNno2lVgxw5fqNGd9z/b61h6LNnqdJqHnBgi9PEzsvjZSt1UOZtjnejaLYUUMn5I35ry2kPGzvb5rh6UYPf/RURp+fJH0dRGiH6zcHtI+17NZLCti+BwjebSRfEWvrxps47f6WYrR85yM0/TN8+Q6Awx/qmtR+nq2t2czH8ti+IQQvyeEkEKIhuoGQORnl+e8bG95r22WYvRcPSla/u4MxWYPg1/cgW977V3SbKNnsxBLNnxCiI3AA8DFascYfgf+N0Zx9mdtr2+NsRSj5+zL0PrXpzCCDga+vBPv7tnlaAthGz2balgOj++/Ar8PyGoHGEEHplsl8pO5bWU1Xp9t/FYXSzF6jsEsbX91EulU6f+tXXgO5CqOt4MZNsvBkgyfEOIhoE9K+VYt46QiiD3QjhYvoOT0Ob0+2/hdOyzW6E0QODyKVAX9v72rYoc0sIMZNsuHkHJ+R00I8QzQUuHSHwL/DnivlDIhhOgBDkkpR+eY50vAl8a/3AucWOyil5kGoOKaVwB7LbNZLesAey1zsZrWskNKGVjopgUN35wDhdgH/BzIjn9rA9AP3CSlHFxg7BEp5aFFPXiZsddSmdWyltWyDrDXMhfX4lq0xT5ASnkcaJrywB7m8fhsbP7/9u4nxMoqDuP492EwjP7QpqBSGBcSidjUIgw3oS7GkomCwKgIaplg0CKHgSIiCIRoUSBR4SIrhJJCCR3IcNMfyUZLxkLaeCGYRQRBoGhPi/cMXIZr997hvvd3p/f3gYF5h3M5D3fm/XHOec+5k9KoWFFH1lJKaRCWPeJbyvZ4H83fHVS/A5BZOhuVLKOSAzLLtay4LMte40sppZUqp7oppcYJL3x9H3erJ8Nrks5KmpN0XNIdQTn2STpfshyWdEtEjpLlcUlaplkIAAAC10lEQVTnJP0jKeSJnaRJSb9IuiBpb0SGkuMDSQuSwrdgSVor6YSk+fL72ROYZbWk7yWdKVlejcpS8oxJ+lHSkW5tQwvfco671WSf7U22J4AjwMtBOWaBjbY3Ab8C00E5oNpn+RhwMqJzSWPAO8AOYAPwhKQNEVmAA8BkUN9LXQFetH03sBl4PvB9uQRstX0PMAFMStoclAVgDzDfS8PoEV/fx93qYLv94z9uICiP7eO2r5TLb6n2RoawPW878qjE/cAF27/Zvgx8AjwSEcT2SeCPiL6Xsv277dPl+7+obvSQ40uuLP4fgFXlK+TekbQGeBh4r5f2YYVvucfd6iLpdUkXgSeJG/G1exb4MjpEoDuBi23XLYJu8FElaRy4F/guMMOYpDlgAZi1HZXlLapBVE+fejKw7Syd9HLcrc7+e81i+3PbM8CMpGlgN/BKRI7SZoZqSnOwjgz9ZAmkDj/LLQiFpBuBT4EXlsxYhsr2VWCirEcflrTR9lDXQiXtBBZs/yDpwV5eU2vhs72908/Lcbd1wBlJUE3pTkvqetxt0Fk6+Ag4Sk2Fr1sOSc8AO4FtrnmvUR/vSYQWsLbtevFIZONJWkVV9A7a/iw6D4DtPyV9TbUWOuyHQFuAKUkPAauBmyV9aPupa70gZKpr+yfbt9keLxufW8B9dRW9biStb7ucAs4H5ZgEXgKmbP/drf3/3ClgvaR1kq4DdgFfBGcKp2qk8D4wb/vN4Cy3Lu48kHQ9sJ2Ae8f2tO01pZbsAr76r6IH8Q83RsUbkn6WdJZq+h21ReBt4CZgtmyt2R+UA0mPSmoBDwBHJR0bZv/lIc9u4BjVAv4h2+eGmWGRpI+Bb4C7JLUkPReRo9gCPA1sLX8jc2WkE+F24ES5b05RrfF13UoyCvLkRkqpcXLEl1JqnCx8KaXGycKXUmqcLHwppcbJwpdSapwsfCmlxsnCl1JqnCx8KaXG+Rcy+ibTOt5HVQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lreg =  LogisticRegression(penalty = \"l2\", C = 1.0,random_state=0, solver='lbfgs',multi_class=\"ovr\").fit(m2X, mY) # create and fit a regularized logistic regression model to the quadraticly expanded features\n",
    "\n",
    "\n",
    "# plots the probability as before\n",
    "logistic2z_reg = lreg.predict_proba(testpoints2)[:,1].reshape(len(x),len(y)) # probability Y = 1\n",
    "f,ax = subplots(1,1,figsize=(5,5))\n",
    "cn = ax.contourf(x,y,logistic2z_reg)\n",
    "ct = ax.contour(cn,levels=[0.5])\n",
    "ax.scatter(mX[:,0],mX[:,1],s=5, c = [\"black\" if t < 1 else \"white\" for t in mY],alpha=1)\n",
    "ax.clabel(ct)\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.88999096  2.46379404 -0.29996405 -0.02285     0.00337729  0.11771078]]\n",
      "[0.58713525]\n"
     ]
    }
   ],
   "source": [
    "# Run logistic regression on the titanic data\n",
    "\n",
    "titanic_logist = LogisticRegression(penalty = \"l2\", C = 1.0,random_state=0, solver='lbfgs',multi_class=\"ovr\").fit(X, Y) # create and fit a logistic regression model on the titanic data\n",
    "\n",
    "\n",
    "# Look at the coefficients (weights) in the model. Are they meaningfull? \n",
    "# Do you need to change the way any of the features were encoded?\n",
    "print(titanic_logist.coef_)\n",
    "print(titanic_logist.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implement Logistic Regression (Optional)\n",
    "Recall for logistic regression we are trying to find (assuming we have encoded $Y$ as $\\{-1,1\\}$)  \n",
    "\\begin{equation}\n",
    "\\boldsymbol{w}^* = argmin_{\\boldsymbol{w}}\\left( \\sum_{i=1}^n \\ln(1+e^{-y_i\\boldsymbol{w}^T\\boldsymbol{x}_i})\\right)\n",
    "\\end{equation}\n",
    "\n",
    "This is a convex optimisation problem in $\\boldsymbol{w}$.\n",
    "\n",
    "We can solve it using gradient decent (or an optimisation library)\n",
    "\n",
    "**Exercise:** *Implement logistic regression using scipy's optimisation library and run it on the Gaussian mixture data mX,mY.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.70838718])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w0 = np.random.random((dataX.shape[1],1)) \n",
    "x_1 = dataX[0]\n",
    "y_1 = dataY[0]\n",
    "def loss(w,X,Y):\n",
    "    sum_log = 0\n",
    "    for idx, j in enumerate(X):\n",
    "        sum_log += np.exp(-Y[idx] * np.dot(w.T,j))\n",
    "        \n",
    "        \n",
    "    return np.log(1+sum_log)\n",
    "\n",
    "# print(w0.T.shape)\n",
    "# print(w0.T)\n",
    "# print(x_1.reshape(3,1))\n",
    "# print(x_1)\n",
    "# print(np.exp(-y_1 * np.dot(w0.T,x_1)))\n",
    "loss(w0,dataX,dataY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.10653611  1.79537059  1.83043164]\n"
     ]
    }
   ],
   "source": [
    "# implement logistic regression using the scipy's optimization library and run it on the gaussian model data\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "# copy input so our modifications don't effect original data\n",
    "dataX = mX\n",
    "dataY = mY\n",
    "\n",
    "# encode mY as -1,1\n",
    "dataY[mY==0] = -1\n",
    "\n",
    "# add a column of all ones to mX to allow us to fit an intercept\n",
    "dataX = np.hstack((np.ones((mX.shape[0],1)),mX))\n",
    "\n",
    "\n",
    "# implement the loss function\n",
    "def loss(w,X,Y):\n",
    "    sum_log = 0\n",
    "    for idx, j in enumerate(X):\n",
    "        sum_log += np.exp(-Y[idx] * np.dot(w.T,j))\n",
    "        \n",
    "        \n",
    "    return np.log(1+sum_log)\n",
    "    \n",
    "\n",
    "# start the optimization with randomly guessed weights    \n",
    "w0 = np.random.random((dataX.shape[1],1)) \n",
    "\n",
    "# runs the optimisation\n",
    "optimal = minimize(loss,w0,args=(dataX,dataY),method=\"BFGS\")    \n",
    "w = optimal.x\n",
    "print(w)\n",
    "\n",
    "# how does this compare with the coefficients you saw using Sklearn? \n",
    "# try refitting the sklearn logistic model with a very high value for C (like 10000)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimisation method we are using (BFGS) needs to know the jacobian (gradient of the loss function with respect to w). Since we didn't supply it, python is approximating it numerically. We can speed things up by supplying it.\n",
    "\n",
    "\\begin{equation}\n",
    "L(\\boldsymbol{w}) = \\sum_{i=1}^n \\ln(1+e^{-y_i\\boldsymbol{w}^T\\boldsymbol{x}_i})  \\longleftarrow \\text{ loss function}\\\\\n",
    "\\nabla{L} = [\\frac{\\partial L}{\\partial w_1},\\frac{\\partial L}{\\partial w_2}, ..., \\frac{\\partial L}{\\partial w_D}] \\longleftarrow \\text{ definition of gradient}\\\\\n",
    "\\frac{\\partial L}{\\partial w_j} = -\\sum_{i=1}^n x_{ij} \\frac{ y_i e^{-y_i\\boldsymbol{w}^T\\boldsymbol{x}_i}}{1+e^{-y_i\\boldsymbol{w}^T\\boldsymbol{x}_i}} \\longleftarrow \\text{ result of taking partial derivative of loss function with respect to weight $j$}\\\\\n",
    "\\end{equation}\n",
    "\n",
    "**Exercise:** *repeat the previous exercise but supply the Jacobian to the minimizer.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      fun: 5.00682707434123\n",
      " hess_inv: array([[ 0.09804117,  0.21480428, -0.14708873],\n",
      "       [ 0.21480428,  0.62279793, -0.44152355],\n",
      "       [-0.14708873, -0.44152355,  0.33837035]])\n",
      "      jac: array([ 30.39840799, -31.33202553, -25.52436333])\n",
      "  message: 'Desired error not necessarily achieved due to precision loss.'\n",
      "     nfev: 107\n",
      "      nit: 2\n",
      "     njev: 95\n",
      "   status: 2\n",
      "  success: False\n",
      "        x: array([0.34952518, 1.2465903 , 1.33759444])\n",
      "[0.34952518 1.2465903  1.33759444]\n"
     ]
    }
   ],
   "source": [
    "# implement jacobian\n",
    "\n",
    "def grad_loss(w,X,Y):\n",
    "    sum_log = 0\n",
    "    for idx, j in enumerate(X):\n",
    "        nom = Y[idx]*np.exp(-Y[idx] * np.dot(w.T,j))\n",
    "        denom = 1 + np.exp(-Y[idx] * np.dot(w.T,j))\n",
    "        sum_log += j * (nom/denom)\n",
    "        \n",
    "        \n",
    "    return -sum_log\n",
    "    \n",
    "# start the optimization with randomly guessed weights    \n",
    "w0 = np.random.random((dataX.shape[1],1)) \n",
    "\n",
    "optimal = minimize(loss,w0,args=(dataX,dataY),jac = grad_loss, method=\"BFGS\")    \n",
    "print(optimal)\n",
    "w = optimal.x\n",
    "print(w) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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